He would probably have to hit better than he did back then but my guess is he would (hit better that is).
Jose Iglesias has had a decent career as an all-glove starting shortstop (almost identical numbers relative to competition, too), and his glove is nowhere near the level of Ozzie's.
I agree that Ozzie would probably hit better. I'm not sure he'd really have to though to be a regular for quite a number of years.