SixStringSlinger
Poster Extraordinaire
Yes it does lol
But I suppose I shouldn't explain how if you're deadset in that belief. Anyways, there's tons of threads and videos out there that proves it.
What exactly do you mean by "action"? Because that term usually refers to the height of the string off the fretboard. I can see how string tension could be affected by a flipped headstock, but not action as I've defined it.