You can check in at ANY AA counter for ANY AA flight from ANY AA terminal. There is no impediment that prevents your bag from travelling from B/C check-in to gate A(whatever).

All terminals are connected airside, so you can clear TSA in any terminal and walk to your gate. Just make a right after TSA and keep going until you get to A.

OK, maybe checking a bag at F for a mainline flight would be a problem, but that's a silly thing to do under any circumstances and I haven't tried it (and it isn't an option here anyway).