I was wondering about this. In my case, however, it's not the same time of departure, just the same day.
I have a paid business XXX-LHR-DUB with LHR-DUB departing until late evening (8hr LHR connection). I'm considering skipping that one and going to NCE instead 2hrs after landing in LHR (avios award). Will BA notice that I have two BA flights on the same day and cancel one of them...or both?