SVA did this very thing with a group of ex-Eastern Air Lines pilots a few years ago.
Called 'em all into the office (about forty in number) and they were told, point blank...'any more discussion about any sort of 'union' or 'association' and we will terminate the lot of you, right now.'
All 'union' discussion ceased, forthwith.
Don't care what company you're in...or the country, airline managements today have the upper hand.
The stack of applications in the HR department would, I firmly expect, cover all vacancies.
Think otherwise?
Try it and see.
BALPA?
A BA (and perhaps a few others, BMI, for example) entity, in all respects.
Otherwise, a paper tiger, nothing more, nor less.