AA most certainly knows that your card was declined and that you have not yet paid for the purchases. In due course, you will likely hear from AA, perhaps if you try to use the same card for any other AA purchase, including a ticket. You can call Customer Service to settle up if you want to avoid the bother.

If your question is whether the FA knows on the spot, the answer is no. Those machines are synched after arrival. The fraud rate is low and most customers who inaderdently stiff AA do make good, so it's not worth the cost of WiFi and a cellular linc.