I’m surprised there isn’t a more definitive answer. I CAN’T be the first person to think of doing this.
I’m not seeing anything in the rules that would disallow it. A carrier is a valid landing space for any fighter or tac bomber, the rules don’t mention ensuring sufficient capacity for landings.
It is pretty much definitive. It says you can’t send them on suicide missions (or some wording akin to that).
As the others have mentioned. You need to have a potential landing spot to send aircraft to fight. If only having 2 potential landing spots (assuming perfect rolls), you can only dedicate two air planes.