I don't see Rondo and White fitting in well together. Rondo has the ball in his hands as much as any point guard in the league and White is used to controlling the ball like a point. I'm not saying White can't adjust but the things that made White productive in college aren't set up for him here.
Then there's the shots Rondo creates for his bigs, which are usually jumpshots or alley-oops. Neither are a part of White's game. Could Rondo play off White? Sure he could but Rondo hasn't moved a lot off the ball since his first two years in the league. If he didn't move off the ball with Pierce, Garnett and Ray, all very able passers, sharing the floor with him, I doubt it's going to be White who is going to resuscitate Rondo's inner Avery Bradley.
I like the idea of White facilitating the second unit though. That could work.
Seeing the deterioration in the Celtic's offense the last three years has been awful to see and makes me really frustrated with Ainge. Lack of shooters, no backup point ever, Paul slowing and not getting to the free throw line much and no one else having the ability to make up for dip, lack of guys who can create their own shot; maddeningly slow pace, no offensive rebounding.