If I remove my foam from my crash bar will my bumper drop

 

Nope.

 

No but it won't fit properly. The bumper is held onto the car by 6 nuts on the top of the bumper, and 2 clips on the sides, fixing it to the fender. The bumper is kinda pulled inwards buy those nuts and clips and pressed against the foam, so that it can't move. Without it, it won't be as solid/stable as it used to be.