There's nothing that inherently prevents matching a catapult to a propeller aircraft. A carrier's catapult is re-set for every single launch, based upon the weight and type of the airplane that needs launching.
The catapult shuttle attaches to the nose gear of the aircraft, so there's no interference with the engines at all.
I'm pretty sure they do in fact use catapults for E-2 aircraft. It can't hurt, and can only help by making it safer. But Naval operations is not my specialty, I'm sure someone else knows the answer to this.