Right but BA can only void the coupons for which it has control (i.e. the BA flights). Typically when one is a no-show the operating airline notes the failure to fly and voids the rest of the coupons that they have under control.

The key link in the process is what happens when BA returns the coupon to AA when the OP no-shows. Given that the interline process is complicated, it's hard to say how quickly the coupon is returned and what action AA takes with the returned coupon. It has been my observation with other interline agreements that typically when the validating carrier (owner of the eticket) and operating carrier are different, the validating carrier won't cancel the eticket when a coupon is returned to them. What happens in this specific case, who knows.

So like I said, if I were a betting man I'd say it's possible. But having to talk to an AA agent in LHR to check luggage would mean all bets are off.