It's been explained a million times, it's very simple.
BA can do what it wants. You will be able to claim against BA at an employment tribunal. They have the power to award you damages, a pittance, but not to make BA give you your job back.
Vote yes, go on strike, get sacked, get a tribunal date, get another job to pay your bills in the 12mth wait, get damages, get on with life outside BA.
It's that simple. For clarity ask your reps why they attempted to get de-rostered for the last dates?