Jared Sullinger, Brandon Bass, Jeff Green, Kevin Garnett, Chris Wilcox, Fab Melo, and Jason Collins are our bigs right now. These are my estimates to individual minutes (excluding Sully) :
KG - 30-31 minutes
Jeff Green - 5-10 minutes
Chris Wilcox - 5-10 minutes
Fab Melo - 5 minutes
Jason Collins - 0-5 minutes
Brandon Bass - 20-25 minutes
There are 96 minutes needed to be played for the posts.
Theoretically, the team would have around 65-86 minutes. At worst, Sully would get around 10 minutes. At best, he'd have 31.
I think it would be very possible for Sully to see a lot of playing time, given he impresses well and gets off to a good start. Then again, his minutes could easily reduce if he is outplayed by Wilcox, Bass, etc. Unless we sign another big, it's very possible Sully could see the court a lot, while keeping everybody happy.