That foam will absolutely compresses. Your question said 'over time'. No, it does not compress over time. But, you do not need 'over time' for it to be a problem.
This is what will happen:
- You will install the foam in the block using some clever method of keeping the foam in place until the drywall is hung.
- You will blue bolt the drywall to the block with the foam between.
- You will coat the bolt with mud, finish, and paint.
- You will lean on the wall which will compress the foam and pop the mud.
So don't do it!
Also... The block will sweat. The foam will keep the water off of the drywall, but it will not allow the water to evaporate creating a wet situation which will, in time, manage to saturate the drywall.
So don't do it!
Blue bolts are expensive. Oh and keeping the foam in place and... Wow and...
So don't do it!
Here is what people do...
- Blue bolt 3/4" furring strips to the drywall. Better yet, use 2x2s.
- 1" drywall bolt the 1/2" drywall to the furring strips. Better yet, use 5/8 drywall to keep the drywall flat where you will be missing a top and bottom plate and use 1-1/4 inch screws to attach it to the 2x2s.
- Do not allow the drywall or the furring strips to directly touch the floor.
- Install floor trim to cover the gap between the floor and the drywall.
This creates an air gap so that the block can breathe.
Remember: The block needs to breathe or it will become wet. So don't create a bottom or top plate and don't let anything touch the concrete floor save the trim on top which will probably be 3/8 off of the floor to allow for carpet.