Depends. The thing with poly is that is a surface coat only. It doesn't penetrate into the wood the way a traditional oil finish does, so it will wear faster and may chip, especially if you put it on too heavy. If you've been around boats much you've probably noticed the wear characteristics of spar poly/varnish on masts and other woodwork. Spar varnish is an excellent UV protectant which will (with annual or bi-annual renewal) help wood in constant sunlight retain it's original color. That said, I'd suggest 3 or 4 coats if you plan on exercising the gun much.
I would have suggested Waterlox as a better finish for a stock if I'd known about this earlier, but unless you want to sand it down to bare wood again it's a little too late now. Sorry. http://www.waterlox.com/