Yes, Ray would have a gun if he was a Mountie in Canada... in fact, one of the "glitches" of the show was that Fraser, as a Mountie, would have automatically had his gun licence accepted. So I've always chosen to think that he has made a conscious decision not to do the little bits of paper work to allow him to have a gun for some reason of his own. (Perhaps he's worried, like his sister Maggie, what he might do with a loaded gun.) As far as I understand it all he would have to do would be go down to a shooting range and demonstrate competence with his weapon.

But yes... if Ray became a Mountie he would carry a weapon.

So... have you looked into it? Would it be possible for an American cop to become a Mountie?