The larger issue is why are you doing this? If you are going to have a battlecarrier that's acting as your combat air patrol provider, that would suggest that your own carriers either can't provide it, or, you need to load your fleet carriers with as many strike aircraft as possible to hit the enemy as hard as possible, which means you're offloading the fighter duties to another ship. Which then raises the question of why are you doing that, and the only real answer for why you would do that instead of having a dedicated battleship and a dedicated aircraft carrier or two is that you're horribly outnumbered and you're looking to eke every last margin out of your fleet. And if you're that desperate, you have much, much larger issues to address than could possibly ever be solved by a battlecarrier carrying a squadron or two of fighters.