I am sure that BA/AA will communicate fast enough to void his return
But I agree with the other posters that more disconnected airlines often do not. If you buy a multi-airline ticket with airlines not in the same alliance, it sometimes seems like there's no communication at all; e.g. UA/podunk airways. In the past I've missed a segment, voiding the remainder of the ticket on UA, but not affecting the FJ segment even with weeks between the missed segment and the podunk segment.