Let me preface this by saying that the only way Jared Sullinger will destroy his draft stock is if he goes up against a talented big man and gets dominated. The way I see it is that there are only three places that this could take place.
The first place would be in the Elite Eight against Syracuse and Fab Melo. If Sullinger were to struggle against a less-talented big man like Melo, people would start to wonder if he really has what it takes at the next level.
The next place would be the Final Four against North Carolina. With John Henson and Tyler Zeller roaming the post for UNC, Sullinger could possibly have a hard time against them. Obviously, Sullinger is much, much stronger than either Henson or Zeller, but if they have their way with him, his stock could drop dramatically.
Finally, Ohio State would have to make it all the way to the championship game against Kentucky for Sullinger to have his stock affected. If Anthony Davis was to simply dominate Sullinger, NBA teams would have to be wary of the big man from Ohio State.
Other than those three scenarios, Sullinger would likely still end up as a top-10 draft pick. However, if one of those events described above takes place, we could see quite the fall from Sullinger come draft day.