You don't specify, but I presume you are in different PNRs.

AA are not BA; they will simply waitlist you on the following flight; what they won't do is proactively protect you in case of delay (or, in this case, change for free the flight to one that meets the MCT after the BA schedule change) with a confirmed seat.

If you are in the same PNR, the automation of whomever issued the ticket should notice the issue and fix it (often a manual process, depends on GDS/airline/travel agent).