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Quite obviously, if they don't have language they will not acquire language from books. The gap between not having and having language is simply too great. Therefore I will assume that they already have language, and I will concentrate on the possibility of learning a foreign language from books.

Second, simply learning a foreign language from books is well-known to be possible. After all, there are many millions of people on Earth who can read Latin, or Ancient Greek, or Biblical Hebrew; and there are quite a few people who can read Sumerian, or Akkadian, or Hittite, or Ancient Egyptian. Those languages do not have any native speakers, and everybody who can read them has learned to read them from books.

Moreover, languages such as Hittite or Tocharian were deciphered from written materials without the benefit of any Rosetta stone or other dual-language inscriptions; so we know that it is possible, in special circumstances, to acquire an unknown language based only on written materials in that language.

This answer will concentrate on the possibility of learning the spoken form of a language based only on written materials.

In fiction

Famously, E. R. Burroughs's Tarzan of the Apes learned written English from the books he found in the ruins of the cabin built by his deceased father. Of course, he had no way of learning to speak English, since his knowledge was limited to the written form.

(The novel is freely available in multiple formats at Project Gutenberg.)

Actually there is a nice sequence in the book delving upon the difference between the spoken and written language. One of the first "civilized" persons Tarzan met was a Frenchman, lieutenant Paul D'Arnot:

D'Arnot spoke to him in French, but the man only shook his head—sadly, it seemed to the Frenchman.

Then D'Arnot tried English, but still the man shook his head. Italian, Spanish and German brought similar discouragement.

D'Arnot knew a few words of Norwegian, Russian, Greek, and also had a smattering of the language of one of the West Coast negro tribes—the man denied them all.

After examining D'Arnot's wounds the man left the shelter and disappeared. In half an hour he was back with fruit and a hollow gourd-like vegetable filled with water.

D'Arnot drank and ate a little. He was surprised that he had no fever. Again he tried to converse with his strange nurse, but the attempt was useless.

Suddenly the man hastened from the shelter only to return a few minutes later with several pieces of bark and—wonder of wonders—a lead pencil.

Squatting beside D'Arnot he wrote for a minute on the smooth inner surface of the bark; then he handed it to the Frenchman.

D'Arnot was astonished to see, in plain print-like characters, a message in English:

I am Tarzan of the Apes. Who are you? Can you read this language?

D'Arnot seized the pencil—then he stopped. This strange man wrote English—evidently he was an Englishman.

"Yes," said D'Arnot, "I read English. I speak it also. Now we may talk. First let me thank you for all that you have done for me."

The man only shook his head and pointed to the pencil and the bark.

"Mon Dieu!" cried D'Arnot. "If you are English why is it then that you cannot speak English?"

And then in a flash it came to him—the man was a mute, possibly a deaf mute.

So D'Arnot wrote a message on the bark, in English.

I am Paul d'Arnot, Lieutenant in the navy of France. I thank you for what you have done for me. You have saved my life, and all that I have is yours. May I ask how it is that one who writes English does not speak it?

Tarzan's reply filled D'Arnot with still greater wonder:

I speak only the language of my tribe—the great apes who were Kerchak's; and a little of the languages of Tantor, the elephant, and Numa, the lion, and of the other folks of the jungle I understand. With a human being I have never spoken, except once with Jane Porter, by signs. This is the first time I have spoken with another of my kind through written words.

Tarzan then learns the "language of men" from the Frenchman, innocently associating the French spoken words with the English written words:

And so D'Arnot commenced at once, pointing out familiar objects and repeating their names in French, for he thought that it would be easier to teach this man his own language, since he understood it himself best of all.

It meant nothing to Tarzan, of course, for he could not tell one language from another, so when he pointed to the word MAN which he had printed upon a piece of bark he learned from D'Arnot that it was pronounced "homme", and in the same way he was taught to pronounce APE, "singe" and TREE, "arbre".

Fortunately, lt. D'Arnot realized his mistake and eventually Tarzan learned both spoken English and spoken French.

In reality

The following real-history examples show the difficulty of reconstructing a spoken language from written materials only.

1. 
   

   The first example is the reconstruction of older forms of Chinese. The Chinese language(s) have always been written with their infernal characters, so we (for suitably chosen meanings of the word "we") can understand texts written in Old and Middle Chinese; the problem is that Chinese characters do not have any direct relationship with the sounds made by a human speaking the language, to the effect that reconstructing the spoken form of the language is a very difficult problem.

   
   
   

   Old Chinese was spoken until well into the first millennium BCE, and evolved into Middle Chinese. For comparison, consider that we have much less trouble reconstructing the spoken form of Homeric Greek, which is roughly of the same time depth; the difference being that Greek was written alphabetically, with a script which represented the sounds of the words and which was never forgotten.

   
   
   

   (Middle Chinese, spoken up to the middle of the 1st millennium CE, is a little easier to reconstruct because we have some materials describing some aspects of the pronunciation of words, mostly for the purpose of enabling writing formally correct poetry; the problem remains very difficult, but at least it's not hopeless.)

   
   
   

   The end result is that we have multiple concurrent attempts to reconstruct the sounds of Old Chinese, reconstructions which are only slowly coalescing into a fuzzy consensus. Remember that this is about a language which has living descendents spoken by a billion people!

   
   


2. 
   

   The second example is about the Hittite language, spoken in Asia Minor (modern Anatolia, in Turkey) around the middle of the 2nd millennium before the common era. The decipherment of Hittite by Bedřich Hrozný is a fine story in itself, but it remains for another time. What's interesting in the context of this question is how many holes are in our ability to reconstruct spoken Hittite.

   
   
   

   Hittite was written with the Akkadian cuneiform script, so that for the most part we know how it sounded. The problem is that in their script the Hittites used quite a few Sumerograms, which represented common words without any link to the spoken form. (Think how in English we use symbols such as 7, &, %, $, and then imagine that we never wrote seven, and, percent or dollar.)

   
   
   

   For example, we have not found any Hittite text containing the word for "horse" written phonetically; in all the texts in which it appears it is written with a Sumerogram. The end result is that while we can read Hittite texts, there are quite a few common words which we have no idea how they sounded.

   
   

A ray of hope

As we see, it is very hard to reconstruct the spoken form of a language when all one has are texts written in a script which does not represent the phonetics of the language. If the script does represent the phonetics of the language, even as imperfectly as English script, and if the script was not forgotten, then the problem becomes tractable.

For example, there are no native speakers of Ancient Greek, or Latin, or Biblical Hebrew; but those languages were written with scripts which represented the phonetic reality, and the scripts themselves were never forgotten. We can be pretty confident that our reconstructions of the spoken forms of Ancient Greek, or Latin, or Biblical Hebrew are good enough.

Even when the script was forgotten, there is a ray of hope if the script reflected the pronounciation and the language left known descendants; for an example, consider Ancient Egyptian. While the reconstructions of the spoken forms of Ancient Egyptian are extremely imperfect and quite approximative, they are nevertheless light-years ahead of the reconstructions of Old Chinese. (The main problem is that Ancient Egyptian script, like all Semitic scrips, does not represent the vowels; so that while the consonants are pretty well reconstructed, the actual pronunciation is still quite fuzzy.)

And Ancient Egyptian also provides an example of a way out. Since the actual pronunciation of the words is uncertain, almost nobody attempts to use it. People who study Ancient Egypt have developed a conventional pronunciation, which, while known to be wildly different from the sounds made by the ancient Egyptians themselves, is good enough to enable communication between Egyptologists.

For example, the name twt-ꜥnḫ-ı͗mn is conventionally pronounced /tuːtənˈkɑːmən/ in English, but, in his lifetime, it was likely to be pronounced something like *[taˈwaːt ˈʕaːnxu ʔaˈmaːn]. (Wikipedia, s.v. Egyptian language; the name in question is of course "Tutankhamun".)

In conclusion

In the absence of some form of direct transmission of the phonetic information, the species in question won't be able to reconstruct the pronunciation of English. They will be able to learn written English, and they will be able to develop a conventional pronunciation for use in speech. As a wild speculation, they may pronounce "famously, E. R. Burroughs's Tarzan of the Apes learned written English from the books he found" as "'senaifru 'o 'ol 'tillaibʱfof 'kelvem as kʰo 'eudof 'ro:lmog 'hlukkom 'ombruʒ slan kʰo ta:pf ho saimg"...

As others have also said - No

Interpreting language requires knowledge of language in general, and of related or similar specific languages

Linear B was a script found primarily on Crete. It took generations of study, and recognition of similar patterns in known languages, to begin to break down how it even worked. Only after that work had been done was it recognized that certain differences between the script's uses in different places might indicate place names, and only then was it possible to infer that the language rendered in Linear B was a primitive form of Greek (a known language).

Etruscan is a language we more or less know how to phonetically read. There is one incidentally preserved Etruscan book, many tomb inscriptions, and known influences on Latin from Etruscan. In spite generations of work, and deep analysis into the language's structure, we still cannot decipher what it means. This is in spite of the tomb inscriptions often being paired with pictures which MIGHT be illustrations of what the text is describing. The difficulty is that Etruscan appears to be from a family of languages which is completely unknown in modern times.

English is among the worst of "phonetic" languages to figure out

We pronounce "kernel" and "colonel" the same way. Why? Colonel is from Middle French. Kernel is from Middle and Old English. I don't know if that particular word is an example, but England was conquered by French-speaking conquerors in the 11th century, and Old English (a Germanic language) eventually mixed with the language of the Norman conquerors, leading to a mixture of mismatched words (deer and venison, cattle and beef), and irregular spelling conventions. English has additionally been one of the most promiscuous of languages in generally, borrowing liberally from Latin and Greek, directly and indirectly, also with differing spelling conventions depending on when and by what route the word was adopted. (The "ph" for an "f" sound, for example, usually indicates a Greek origin.)

I could be persuaded that beings of godlike intelligence, given a large enough sample of written English (and maybe an understanding of the anatomy of human mouth, lungs, and vocal chords), might be able to simultaneously infer pronunciation and word-meaning, in sort of the same way that you could fill in the missing numbers in a Sudoku puzzle. For primitive beings who have not yet developed a language? Impossible.

If they don't have /any/ concept of language? No. Until they make the jump to having /some/ way of communicating ideas and concepts to each other, they won't be able to realize the significance of what the books are or store that realization in enough other people to start down the path of what the words may mean.

If they had their own language, they might possibly be able to read it. If there are enough common frames of reference, they may wind up using English as a blueprint pattern to construct their own written language, and if they have enough texts, they might very well be able to reconstruct the meanings of enough of the English words to decipher the rest of the books. This will take quite some time, as they'll need to develop linguistics to do it, and by that time, their own language will be pretty firmly entrenched in their society.

Speak it? Almost certainly not. The written English word has so many bizarre spellings and odd constructions that without someone or something that actually /does/ speak it, figuring out /how/ all these symbols are pronounced would be nigh-impossible. Perhaps if you had english linguistic textbooks and english biological texts and the ability to construct model human mouths, lungs, teeth, vocal chords, and tongues, you might be able to pull off a simulacrum of how the worlds might sound. But if you can do that, your own language is definitely serving you just fine at that point.

This is extraordinarily unlikely, regardless of what some very bad books and movies might suggest.

At the least, it would require a vast number of books with pictures of things, and animations of actions. Quick now, what is an "uxriggabber"?

Worse, many objects are incomprehensible outside of a particular culture and technological level. I had a friend 40 years ago whose sons were being labelled as "slow". Part of the label was based on a picture-based intelligence test. One example they failed was a 1950's era record player console, with the ability to play multiple 33s and 45s (if you don't remember, it was a sort of structure above the platter which would hold records, and you could add a thick cylinder to fit the center hole of 45s) and built-in speakers. The kids were baffled. The parents got fairly irate when they had to explain to the teacher that nobody they knew played 45s, everybody had separate speakers and amplifiers apart from the standalone, single-play turntable. There were more outdated objects as well, but you get the idea. Have you ever seen a button-hook? Do you recognize tack for a plow-horse? A carpet-beater? A thunder-mug? Other than in older movies, where will you learn about old-style (pre-rotary) telephones?

Even then, biology raises major problems. Unless the species is very closely humanoid, there is any amount of room for incomprehension. Does the species exhibit sexual dimorphism, and if so, how? What would the natives make of a corset? High-heeled shoes?

Let's say the natives' sexual cycle involves estrus as with dogs. Most of the time, dogs simply aren't that much interested in sex, and when they are (around a bitch in heat) they don't think about much else. How to interpret love poetry and erotica? Jane Austen? 50 Shades of Grey?

Culture gets in the way. How to make sense of a top hat or spats?

Politics. If they are pack-oriented, what does democracy mean? Or communism.

Finally, English is absolutely horrible in terms of pronunciation of text. G.B. Shaw lobbied for regularization of English orthography without any noticeable success. One of his examples:

Q - How do you pronounce ghoti?
A - "fish". gh as in enough, o as in women, and ti as in emotion.

No

They have no reference to link sounds to letters. Reading could be done sort of using basic children's picture books but without a means of linking actual sounds to letter, speaking is impossible.

I was going to be mention the Rosetta stone which is already mentioned in better details in other answers, but one other example that is similar is the Cherokee written language. Per https://en.m.wikipedia.org/wiki/Cherokee_language (which in turn cites Cushman, Ellen (2011). ""We're Taking the Genius of Sequoyah into This Century": The Cherokee Syllabary, Peoplehood, and Perseverance". Wicazo Sa Review. University of Minnesota Press. 26: 72–75),

Before the development of the Cherokee syllabary in the 1820s,
Cherokee was a spoken language only. The Cherokee syllabary is a
syllabary invented by Sequoyah to write the Cherokee language in the
late 1810s and early 1820s. His creation of the syllabary is
particularly noteworthy in that he could not previously read any
script. Sequoyah had some contact with English literacy and the Roman
alphabet through his proximity to Fort Loundon, where he engaged in
trade with Europeans. He was exposed to English literacy through his
white father. His limited understanding of the Roman alphabet,
including the ability to recognize the letters of his name, may have
aided him in the creation of the Cherokee syllabary.

Per same Wiki link, "Some symbols do resemble the Latin, Greek and even the Cyrillic scripts' letters, but the sounds are completely different (for example, the sound /a/ is written with a letter that resembles Latin D)."

In other words, based on experience with Cherokee (and I believe Rosetta stone), even if the race was able to reverse engineer written english, it is unlike they'd then reverse engineer spoken english unless the books either included a very detailed speech pathology book or ventrioloquist book (or some other book that indicated how sounds should be made with the mouth with pictures etc. and even then, I'm not convinced you'd get 100% accuracy), or some sort of multimedia books.

I agree with Thorne: Given enough source material, your smart primitive society can learn the gramatics, the vocabulary, the informal use of words, but with no sounds it is impossible to figure out pronunciation.
You don't have to look for a primitive smart society to find examples of people learning english from books and having horrible pronuciation: think of japanese or latin american people speaking english today. We may have wonderful use of grammar but our pronunciation will suck most of the time, to the point that a native english speaker will not understand us.
I had no idea that "kernel" and "colonel" sounded the same in english! While reading the answers here I noticed that, for the words I don't know their respective pronunciations, I replaced them inside my head with the spanish sounds for each letter. Result: horrendous and completely wrong pronunciation. Your smart primitive society will replace english sounds with the ones they are used to. Or more likely, they will invent their own spoken alphabet from the books they are deciphering.

Greetings from Perú :D