My mixed metal AA itin last week where US was the first flight, worked more or less. Did OLCI on US and they did in fact include a BP for the subsequent AA flight, except that it was not entirely complete/accurate - different seat from what was on aa.com, no FF#/status, flight# shown as USnnn instead of AAnnn (this was not a code share that I'm aware of). So I wasn't sure if it was in fact valid or not.
Interestingly enough - for my onward flight on CX, when checking my seat assignment >24 hrs out - CX invited me to check in right then and provided BP and lounge invitation. So that was independent of the US and AA flights, not sure why that didn't mess up the 1st 2 flights.