Nope, it doesnt matter what ship you level a sailor on. What matters is that you class them properly and give them experts and vets and a good base etc.

But if you mean, does a pilot grow better when leveled on a CV over a CA or something then no, ship type has no bearing on their ability as pilots.

There is an important decision regarding promoting them though. US fighter pilots have 3 promotions, Fighter at 40, Ace fighter at 60 and Squad leader at 75. If you promote them to Squad leader, you will actually make them worse fighters, it is generally agreed upon that Squad leader promotions are bad.

If you don't promote your fighter at all, (and just keep him at lvl 40 fighter) he will be able to reach a higher maximum ability than other fighters, but at the cost of requiring more vets to take advantage of this potential. Promoting to Ace and not promoting higher than that allows you to reach better ability than Squad leader, and more easily reach some levels of ability than Fighter (with less vets compared to fighter) but still, the potential maximum is lower than fighter.

So, you shouldn't promote to Squad leader, you should either keep them as Fighter (and not promote them after) or promote them to Ace (and then not promote them after that). Which you choose is up to you.