No, it matters whatever the baggage allowance is on the ticket. And if AA issued the ticket, like someone said above, they will have put in two pieces at X kg/lbs.
It's the same when booking a JL domestic flight with BA Avios on 125 stock, you end up getting two pieces of luggage at up to 23kg despite JL domestic fares giving you only 20kg and use the weight system. Or... when booking QR awards with AA and AA "forgetting" to put the luggage allowance on it.

JL can choose to apply their own rules but must at least provide what is indicated on the ticket.