That's what I do (spend most with GCs, just a bit with a CC). I haven't looked in detail at the T&C of the credit card program, but I would guess you would in general lose any travel insurance / cancellation insurance your card may possess (just reasoning by analogy--for car LDW coverage, you must pay for the entire rental using the CC to be coverage). For me it's not really a concern, but YMMV.

That said, I have paid for tickets just using GCs and not gotten SSSSed. I would guess maybe it's because you have to purchase online with an AAdvantage account?