The core mechanics (which were partly lifted from Battlefleet Gothic) make it easy enough to jump between the different systems but your point costs are going to be hopelessly off from one game to the next due to different tech assumptions, so it would be a matter of playtesting to figure out how many White Stars give a good game against a Klingon squadron or House Decados fleet. If you're shooting for casual/friendly games perfect balance isn't really needed, but you'd definitely need to put some work into ironing out cross-setting issues before playing a "live" game.
Probably the hardest element to adapt would be the boarding actions from Noble Armada, or perhaps the way different systems handle (or don't handle) fighters. The grappling part of NA boarding's easy enough to adapt, but the actual troop combat is more of a sticking point. The NA shield/burnout mechanics are probably also a sticking point.
If you're really into crossover gaming, there used to be a backward adaption statting Battlefleet Gothic ships into ACTA: B5 terms out there somewhere, but I can't find it online now. Only ever saw it as a printout at a convention, but I recall it looked pretty good. Amusingly, the guy who had it said he was working on Star Trek next, years before the ACTA: SFB rules saw the light of day.