Took the risk of booking Basic Economy with 3 bags. My wife and I both got to check in one with AA CC and for the last one we were meant to pay at the gate.
Seems to be they can only tell your flying basic economy when boarding if it says boarding group 9 on the boarding pass. Since the CC gets you to group 5 you should be able to get a carry on for free! Just worked a couple minutes ago for us.