I did some testing in single player, I bought a F-CVA and discovered it would let me buy both fighters and PFs for it. In game, my fighterbay shows both fighters and PFs, I can launch them all, but the PF disappears. The PF remains showing as active on the shuttle screen, but is no where to be found in game, nor can it be recovered.
A general statement to all:
Thats because the CVA doesnt carry PF's. You can launch them, but they wont appear in the game. Period.
Same with PF races. If you try and equip a Tender with ftrs, you will be limited to 1 ftr, just as you can only carry 1 PF, and it may not even show in mission.
Bottom line is that if its a carrier, u need to use ftrs and a PF tender must use PF's.
If you don't, then u may launch an illegal loadout and find it may not appear.
One other thing to remember is that in supply dock, there is one clickable button for BOTH ftes and PF's. So you will see them ALL listed. Choose what you are supposed to cary ONLY.