The injunction will, I believe, if granted also render the 3 and 4 day strikes illegal. This means that those who have already been on strike could potentially be now sacked as the action they have taken will have been illegal. Worse still is that BA could also go after the union for the costs incurred as a direct consequence of the strikes. This could potentially damage UNITE terminally, BASSA would almost certainly end up bankrupt.
BA may not go down this line but may use it to force UNITE to capitulate and then hold the option to sack and bankrupt for many years to come until the statute of limitations does its thing.
So it may not matter if you do not strike on Tuesday, you may already have gone beyond the point of no return.
BASSA must be hoping that they got the ballot right back in March or it may already be over for them - terminally.