The Celtics should be looking for a big who can either defend beyond the paint or has offense beyond the paint, preferably both. That's more important than being an above-average rebounder or shot-blocker.
A big who "clogs the middle" because he never leaves it is not a good fit for the Celtics. As long as Doc is the coach, an undersized but mobile big is probably a better option than a stereotypical 7-foot stiff.
Speaking specifically of Mozgov, he seems to be a somewhat athletic but clumsy, foul-prone big man with bad hands who can finish. He has the ability to hit a mid-range jumper, something he would probably be called on to do more often if he became a Celtics, be he seems to be consistently criticized for poor fundamentals.
He seems to me like he can be a decent back-up center, but it would be a mistake to look at him as a potential future starter, so signing him with anything approaching the full MLE seems like a poor allocation of resources.