There may have been some tests (the Mustang was tested, but found too difficult due to approach speed and max tailhook speed being only 5 knots apart), but P-47s were not used operationally from carriers.

The cocooned airplanes were being shipped...that is why they have no props or horizontal stabilzers.

In the Pacific there were great distances in the island-hopping strategy between friendly bases. When a new island and airfield was captured and fighters were wanted there, fighters were sometimes craned onto an escort carrier, which was then more of a cargo ship.

One of your pictures shows it would be impossible to taxi, let alone takeoff or land, when they were so tightly packed.

After some of the planes had been offloaded, it might be possible to takeoff, but I believe they were usually craned off.