I'm not aware of anyone having either pulled out after having accepted, or failed the medical, but don't quote me! If it runs for long enough then statistically it'd most likely happen, but there must be some contingency in place for such events.
Pretty sure the plan was that they took the best candidates irrespective of which FTO they'd be headed to, but really (again) the only people who could confirm that would be BA recruitment.
Like any cadet scheme, they'd want to phase it so that graduates start coming out of the FTOs at the ideal time to fit in around type ratings and line training, so it must make sense to have a relatively even spread between the three schools. That said, if one school had more than the others, the only people it'd likely inconvenience would be those graduates who might end up with a longer wait after finishing at their respective FTO before then carrying on to a type rating. You'd think it might benefit the individual schools to have more students coming in through their doors, which could be an incentive for them to send the right people to Waterside in the first place, but realistically the FTOs can't lose out as they have such a constant stream of self-sponsored cadets anyway, not to mention cadets sponsored by other airlines.