Possibly. I wouldn't be surprised if he doesn't until later. He's got bad handles for a PG and is behind on his point guard training. His defense is superb though. If he doesn't this year, he will definitely in one or two years. With Doc here, Avery will experience a lot of growth.
For those who wanted Derrick Rose or Russell Westbrook on the team, if Avery reaches his potential, he'll be like them, except with a lot better defense.
A lot will lie on this Summer's training for Avery and the Celtics. A lot.