Here is what my doctor told me about my wisdom teeth when I had them pulled out about 5 years ago, or what I remember anyways.
The holes left in your mouth lead directly to your sinuses and the only thing filling those hole until the wounds heal are blood clots. He said if you accidently sucked a blood clot out, such as smoking or sucking liquid through straw could do, then saliva would get into your sinuses and have a chemical reaction with the bones, effectively corroding the bone. He said it was very painful. I have also talked to a person who told me it happened to him and it was one of the most painful experiences he had delt with.
Here is what we know about diving:
You have to clear your ears to avoid ear squeeze as you descend.
If you have to have clear sinuses so that you don't have a sinus squeeze.
My thinking would be that it would be difficult to clear your ears with out pushing the blood clots out of your tooth socket, which could lead to a painful and unnecessary experience as I believe that your eustation tubes and sinues are connected. (I could be wrong there though)