I would think it is a grand slam as long as he touches all the bases. If he stops after he rounds 1st, it's only a single and the only runs scored are the ones that cross home plate.
I'm not an ump or an official score keeper, but if you watch a HR anywhere, the umps are watching to make sure the batter touches all the bases. If he doesn't, I would assume he does not get credit.
Maybe someone with official knowledge could explain.