I see two important open questions:
1. If his shooting ends up being just average, can the Celtics survive with a backcourt that is limited in terms of scoring ability? This was masked somewhat this year because the other three starters (Bass, PP, KG) are all excellent shooters at their positions. But if someone with less offensive ability replaces Bass, we have only two decent offensive options in the starting five.
2. Will his defensive play hold up when other teams can scout him? This year was so unusual because Bradley started playing halfway through, and most teams had limited or no practice time because of the lockout. He surprised everyone. But if Bradley has vulnerabilities (e.g., in the post, or bothering taller 3 point shooters), teams will find them and exploit them.
If those things both can be worked out, I think the Celtics will have one of the best backcourts in the league for the next few years.