Sorry. I thought we were talking about a different 2.2.
If that is the same one they used in the cavalier then yes, the 3800 will bolt right up to it. You will need to get a flywheel. I think you can use a camaro flywheel and get it turned so it will work with the clutch.
A lot of things will need to be swapped around/modded because of the orientation of the motor. It should be a lot of fun.