I very much doubt it. You can read all about it at this special BALPA site. The boring reason is that there is considerable room for compromise, and the interesting reason is that I don't think the pilots are up for it. (This is all about merging - or not - seniority lists; and the terms under which mainline pilots might transfer to OpenSkies - and eventually the other way round.)
The boring and interesting reasons are inextricably linked because the management won't need to give much ground to win over the waverers. One of the special features of a pilot workforce is that it has a far from uniform profile. Although they share basic terms and conditions in common, the most junior staff and the most senior have markedly different vested interests, and hugely different outlooks on life. And there are all shades in between.
OpenSkies makes not the tiniest jot of difference to the more experienced BA pilots. They're effectively being asked to strike for the notional good of others - perhaps some of them will go for it, but I doubt it.
A lot of pilots own BA stock or have an interest in its well-being through one mechanism or another - a strike not only wipes out yet another chunk of BA's extremely hard-earned profits, but it frightens investors for a long time to come. And that's at a time when airlines are about to take a huge whack as recession bites.
The younger pilots have less to lose by striking and, if BALPA's argument is right, vastly more to gain. After all, BALPA says they will face a lifetime of reduced income if BA is allowed to do what it wants to do with OpenSkies. But I suspect those people are just as worried about BA's future in the competitive world anyway. They're watching Star Alliance and SkyTeam moving into LHR, they notice that Silverjet and EOS are still with us, and they've seen the lo-cos come from nothing to dominance in a few years. They're financially savvy and they're probably thinking that OpenSkies sounds like it might be quite important to everyone's good health.
Even over at Pprune, where the dialogue is as ever dominated by the more militant voices, there is a lot of caution.
As a betting man I think there will be a negotiated settlement with very little movement on the management's side. BALPA may win a mandate in the initial ballot - nobody's risking much at that stage - but I think they'll struggle to make it stick.