The P-47 was as much a carrier plane as the B-25s in the Doolittle raid. If a b-25 loaded with bombs could take off of a carrier, it should be a no-problem for a P-47, even though they were known for their relatively long takeoff runs. Landing... well that's a different thing altogether when you are not equipped with an arrestor hook, no strengthened landing gear, and can barely see over the nose.