My advice would be apply and try all that you may in order to get an assessment, pass the assessments, wade through the hold pool and then end up with an offer.
BA isn't the airline it once was. Hell, its a different airline than the one that I applied to three years ago. But so is the industry that we work in. This is a reflection on the industry, not BA.
There'll be no shortage in candidates. The majority fall at the first hurdle. Worry if BA is right for you when someone from pilot recruitment rings you with a start date. By then you should know.