Do teeth have the capacity to heal?
Yes, it can be done to a certain degree.

Cementum is capable of repairing itself to a limited degree and is not resorbed under normal conditions. Some root resorption of the apical portion of the root may occur, however, if orthodontic pressures are excessive and movement is too fast. Some experts also agree on a third type of cementum, afibrillar cementum, which sometimes extends onto the enamel of the tooth.

Cementum is produced by cells called cementoblasts. 

more here:
http://en.wikipedia.org/wiki/Cementum