I love Avery Bradley, and I think he's the perfect fit for this team, and to some degree, I think his "stardom" will depend on the team's success going forward. If he and Rondo can form some semblance of an Isaiah Thomas/Joe Dumars tandem, and they can just bother the heck out of opposing back courts, making it difficult just to get into sets, and the Celtics can continue to go deep in the playoffs, and maybe even win a title with that backcourt, then Avery Bradley will definitely be a "star" in my book.
On the offensive end, though, I'm not sure I ever see him averaging 20+ points per game. He's got the size of a point guard without the handles, and he doesn't seem like he has that scorers mentality like a Monta Ellis or even our very own Jason Terry.
I'm really excited to see his progression as a player, though. I think having him and Lee together is going to be awesome. Those two are going to be competing, not to see who can score more points, but competing over who can lock people down better on the perimeter. That's gonna be fun.