Not likely, and you really don't know what you're talking about here, Josh.
Jetstar and Qantas serve two totally different market segments, and they really don't even interline with each other to any great degree. And Jetstar does have union employees. Unlike here, it's an open shop. If you want to join a union, you join one. There's no exclusivity, either. Some classifications have multiple unions representing the same class of employees.
Go Jet was not set up to be a non-union sub --- they just haven't chosen to vote in a union yet. The pilots from Compass and Trans States did. Should there be a desire to, the unions at Compass and Trans States could easily pursue a single carrier determination since Hulas controls all three entities.
Fact is that just about every airline within an airline or sister airline concept in the US has ultimately failed. Arguably, even Eagle might be seen as a failure since it just wound up being one of the highest cost providers of regional lift. The only example I can think of where there's peace and harmony is Alaska & Horizon. But both are heavily unionized, IIRC.