Task Manager is just an app, I don't think it gets any special treatment really.
If you do get in a spot where Task Manager won't run, you should still be able to press Ctrl+Alt+Del and get the Winlogon security screen, and you should be able to choose the "Log Off" option to log out your account and get out of that state without power cycling the machine.
Basically, Windows already has the sort of background process that can't be pre-empted, but it isn't Task Manager, it's the session manager and logon UI.