Hmm, the way May looks at Drew, I expect she'd kick him where it hurts the way he's talking of her and her Pokemon. Boy, if I was May, I'd probably knock his block off, even if it wasn't in the script.
Well, Ash and Gary may have buried the hatchet, but it was because Ash beat Gary, once and for all, the finale. I can't see how May/Drew would have a Pokemon battle, that's Pokemon battle, not a contest battle. Besides Drew's Roselia and that Masquerin, we don't know his other Pokemon so Drew has a huge edge. Maybe Drew has 6 Pokemon over May's 4 Pokemon.
Besides, Drew would have to big to apologize to May.