Referring to the book "Nutrition and Physical Degeneration" by Weston A Price shows that by removing refined food from the diet of children and supplementing with high-nutrient butters and oils, cavities ceased to grow, and new material grew in the cavities.
He also points out that he did not see a single healthy group of vegetarians in the natural environment, and that for health, the consumption of animal products is required. So, I do not believe that a vegan diet will lead to your teeth healing themselves.