I wouldn't really call it an alarm. No, I don't think you can have one placed in either. I tried when we bought our sunfire. I'm glad I didn't.
Aftermarket alarms aren't super expensive, and much better as far as security.
just had to take my 'factory' alarm out. the siren stopped working 2 years ago and for the last 6 months i've been getting a false trigger everytime i lock the doors, lock them with the remote, alarm trips, unlock and relock and it's ok.
right PITA so i disconnected it.
still have the PASS key system working and i never leave anything of value in the car so the Content Theft Deterrent was really not needed.