I do believe there is a kind of pilot who easily could and should. Take someone for example who has a job offer elsewhere (a lot do for carries in the Middle East or Far East) and hasn't quite handed his/her notice period in yet. I believe there are many in the category but the issue comes down to money.
Well, and it might sound a little fantastical, but if just 100 current pilots put their hands into their pockets to fund a case through one such proxy they would be able to do far more damage than the last 5 years of BALPA negotiations.