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I can manually run the following cmdlet on 10 nodes in AD to register a scheduled task:

Register-ScheduledTask `

    -TaskName "MyTask" `

    -Action $inlinePowershellScript `

    -Trigger $myTaskTrigger `

    -Principal $myTaskPrincipal

I was looking at the ways to automate it on AD level (preferably without leveraging WinRM..)

According to this article and the list of available GroupPolicy cmdlets, it seems like the only way to configure GPO (using PowerShell cmdlets) is by using Set-GPRegistryValue and Set-GPPrefRegistryValue cmdlets.

It seems like following registry keys are available for Scheduled Task:

HKLMSoftwareMicrosoftWindows NTCurrentVersionScheduleTaskcacheTasks

HKLMSoftwareMicrosoftWindows NTCurrentVersionScheduleTaskcacheTree

Given these details, is there a way to perform GPME's computer configuration -> Preferences -> Control Panel Settings -> Scheduled Tasks -> New -> Scheduled Tasks action automatically using $inlinePowershellScript, $myTaskTrigger and $myTaskPrincipal?

You are over complicating this.

Schedule tasks are just xml files. create a task manually, export it and import it to other servers using the scheduled Task cmdlets.

Get-Command -Name '*scheduled*' | ft -a 



CommandType Name                                         Version Source            

----------- ----                                         ------- ------            

Function    Disable-ScheduledTask                        1.0.0.0 ScheduledTasks    

Function    Enable-ScheduledTask                         1.0.0.0 ScheduledTasks    

Function    Export-ScheduledTask                         1.0.0.0 ScheduledTasks    

Function    Get-ClusteredScheduledTask                   1.0.0.0 ScheduledTasks    

Function    Get-ScheduledTask                            1.0.0.0 ScheduledTasks    

Function    Get-ScheduledTaskInfo                        1.0.0.0 ScheduledTasks 

...

Example:

# Create your task 

$A = New-ScheduledTaskAction –Execute 'powershell' -Argument 'Hello, from task scheduler'

$T = New-ScheduledTaskTrigger -Weekly -WeeksInterval 1 -DaysOfWeek Monday,Tuesday,Wednesday,Thursday,Friday -At 8am

$S = New-ScheduledTaskSettingsSet

$D = New-ScheduledTask -Action $A -Trigger $T -Settings $S

$Task = Register-ScheduledTask 'TestTask' -InputObject $D



# View the created task XML

Get-Content -Path 'C:WindowsSystem32TasksTestTask'  | Out-GridView

Get-ChildItem -Path 'C:WindowsSystem32Tasks'



Export-ScheduledTask 'TestTask' | 

out-file '\TargetServerc$publicTestTask.xml'



Invoke-Command -ComputerName 'TargetServer' -ScriptBlock {

    Register-ScheduledTask -Xml (Get-Content 'C:UserspublicTestTask.xml' | out-string) -TaskName 'TestTask'

}

Just use a list of servers in a loop the registration