Would a PUA - PU be able to find the equivalent of some of the principles of game that are nearly universal? Or would it just be a catalogue of culture specific hacks?

Many facial expressions, and many components of body language are human universal. Certain things are always signals of relative status or changes in status, certain things always assert dominance, etc.

People are also always universally interested in themselves, more than anything, and therefore respond greedily to a good listener. People universally want to be important themselves, and usually give off clues as to what ways they want to be made to feel important.

These are just some random social universals off the top of my head. (Universal to neurotypicals, at least, with subsets that still apply even to non-NT's.)