I doubt it.

Jumpseat agreements today are negotiated by company, and serves as a benefit to all involved. I have union pilots ride my jumpseat all the time, and if union pilots began denying me I would do the same. I know that there are more than a handful of pilots of legacy carriers that live in the outlying cities we serve and commute to work on us, just as many of us here at skyw rely on union carriers for the same. To begin denying jumpseats for this union/non-union thing would just amount to a stupid pi$$ing contest that would create an undue hardship for alot of people.