Heres an experiment the Australian Navy did - Aircraft Carrie Subs -

The Royal Australian Navy Skyhawk, being an all-purpose aircraft, was the subject of a 1970s experimental sea trial of an A-4 on board a Royal Australian Navy submarine. There was no objection from the aviators to operating the Skyhawk from the somewhat limited deck space of the submarine. A problem with the Skyhawk's turbine cavitating while underway submerged was overcome. The diesel catapult worked just fine. However, the experiment was abandoned when the submarine's XO objected to the jet blast burning the paintwork off the sail.
Photograph courtesy of the Australian Naval Aircraft Museum: Mark Clayton, Director;, Windy Geale, Curator

I would also add that it would most probably be a great April Fools topic.

......and instead of the standard 'landing gear' they were equipped with HSP's (High Speed Pontoons), also experimental.