There's no issue with fitting an arrestor hook to a tricycle gear airplane, Witness the myriad of tri-gear jets.
That said, most have short landing gear and none of them have a propeller spinning out front. The Tigercat had props, but it also had a nosewheel running interference for the arrestor cables. However, there ARE example of tri-gear airplanes with props out front. It isn't single engine, but the Fairey Gannet has propellers out front of the nose wheel and didn't have any issues.
Granted they were a twin engine and had shorter props than ti would have had if the twin engines had been a single. But it gives you an idea that is was certainly possible.
The Breguet Alize was a very similar airplane, but it had a single turboprop, so we can say a single-engine front prop, tri-gear airplane was possible and practical. Whether or not is was practical in the WWII timeframe is another question.
As for a pusher setup, I do not think a pusher prop with the nosewheel raised at landing attitude would have been practical at ANY time on a carrier due to the prop being VERY close to the runway at touchdown, coupled with the need to raise the arrestor cables so the hook can grab them as it passes them.