To be honest I don't think the injunction does make the strike illegal. An injunction is granted on the balance of probabilities - so the judge thinks it is likely that the ballot was improperly conducted - but a full trial would be needed to decide the issue. To be sure, given that the injunction was granted (but it might be overturned) I think BA would have a good chance of winning such a trial (although that "good" chance would be reduced if Unite win on appeal) - and then I understand the strikers could be exposed as having taken part in illegal action.
Personally though I doubt BA will actually take this course of action. But they might threaten it to prevent any further strike action or ballots. To be honest, unless Unite do get the appeal and win it, this dispute is over and BASSA are finished. The protected period runs out after 12th June and, even if there is a new ballot on the same issue, as far as I am aware this won't be extended. So even with another legal ballot strikers could still be dismissed after that date anyway.