Per experience last month at JFK, on a flight to Mexico (so "domestic"-ish, in the sense of upgrades and service), no paid airport upgrades are allowed, nor we ever offered paid upgrades in the app before check-in. My partner (a BA Gold) asked at the lounge, and was told no changes to the ticket was allowed. We got everything else-- Flagship (or whatever it's called now) check-in, checked bags, group 2 boarding, lounge access, and MCE seats. But if you want the possibility of a cheap upgrade, you'll need to pay extra for the regular main cabin fare.