Absolutely yes. It would be silly not to take full advantage of his free baggage allowance. Nobody is going to open his bags and, of one of them really belongs to a woman in your party, announce publicly that he's a cross-dresser or even ask him how he looks in that skirt.

By the way, you didn't say when you're flying, but it might be worth it for another member of your party to get this or a similar credit card if there's time and his/her credit is good enough to get fast approval. Even if the card has an annual fee, you could probably save more than that in checked baggage fees. Do the arithmetic and send in an application.