Well sure, 'cause Bargnani didn't play college ball.
Oh, wait, you said "productive."
There are a number who wouldn't meet the rebounding criterium, such as Hawes, Hollins and Frye. But even all of those guys managed to squeak past 2.0 blocks per 40. Finding a C who is that weak of a shot blocker is pretty hard.
But I'm assuming that, if we take him, it will be as a point player, and that you're looking at the wrong stats. He gets 4.4 assists per 40, and you probably can't name another big currently in the NBA who topped that his last year in college. JT was good that way, but he only got 3.1/40.
Not that I like the idea.