Yes they would almost certainly rebook you. The app or ba.com would show your new itinerary, or you might be handed an envelope as you exit the aircraft. They pick the best option chosen by their algorithm, usually before you even ask (and note - this treats AA and BA flights exactly the same) but you could still queue/call to ask for something different if you prefer.

Note this only applies if it’s on one ticket. If not, FTV the domestic now and get the train down.