You can have your case exhaust air over the radiator, sure. Usually this doesn't happen, though, because case air is going to be warmer than outside air, and you want the coldest air possible going over your radiator.
Often back case fans exhaust air because that's the most efficient way to plan out case airflow, but I have a top rear fan that intakes. Nothing wrong with back fans pulling air in as long as you equalize everything.