Don't know about cash. The official line from some AA agents is somewhat unclear, and contradicts the information received from other AA agents. IME, CC restrictions regarding billing address only apply if buying by phone; when payment is made in person, and the name on the cc is the same as that of the pax, and you provide photo id, the billing address does not matter. YMMV (big) so it would pay to check and recheck in advance.

By the way, cash, even if accepted, is likely to buy you a lot of hassles down the line.