yuripa87, welcome from lurk mode.

Yes, it would be possible to upgrade using Avios, and worst case is that you have to change the earning FFP back to AA afterwards if your BAEC number gets associated - the upgrade wouldn't get taken away once ticketed.

However, you would need award availability on the flights, and - even if that's confirmed - whilst your points are transferring from Amex/Chase that availability might well disappear ... at which point you'd have no way of transferring them back. There is no such thing as a hold on award flights whilst the miles arrive - they must be there for deduction at the time of booking. I'm not sure that's a risk I'd be prepared to take in your situation - F availability is fairly rare, certainly for TATL, and so tends to get snapped up quickly.