the scheduled task should have configuration option for 'run with highest privileges' to avoid UAC blocking the script. I've got no valid testing environment right now, but I think that option is not availabale for tasks scheduled by GPO
A startup script will allow running as "system", perhaps this security context has enough privileges?
However, I would strongly advise against running any scheduled task with a user that has domain admin privileges. Consider what could happen if the target script is maliciously replaced!
Also note from
this KB:
"This password is stored as part of the GPO in SYSVOL and is discoverable, although obscured. If you choose to store passwords in preference items, you should consider creating dedicated accounts for this purpose, and never store administrative passwords
in preference items."
If you tell us what exactly the script does, we might be able to help you to figure out how to apply the script or setting to all needed computers.