Sometimes AI aircraft will land and then launch in missions that I have made. This occurs when they didn't take off properly in the first place.
Most commonly they will jump off the elevator instead of taxiing to the cat and the LSO will say 'bolter!'. They then come round, land and THEN taxi to the cat and launch.
More rarely AI aircraft will start in mid-air (with their gear down) around the carrier instead of on the deck and then come in to land, taxi and launch.
This only happens when there are a lot of aircraft and events in the mission.