There is a constant flow of fluid from the gut into the teeth.  Nutrients are transported from the stomach through the bloodstream to the tooth pulp chamber where they supply the dentinal fluid with nourishment.  This is an important conceptualization to grasp in order to understand the nature of tooth health and what you can do to promote a mouthful of healthy teeth.  Healthy digestion, the premiere goal of Ayurveda, is what keeps teeth healthy, whole, and white.        

Dentinal fluid  provides nutrients and minerals to the teeth and flushes toxins out. The movement of the dentinal fluid goes from inside the tooth outward in a centrifugal fashion. When a tooth is compromised, even more fluid rushes to repair the tooth.  

However, when the flow of dentinal fluid is interrupted or not strong enough because of poor digestion and toxins in the bloodstream, the movement inside the tooth reverses and becomes centripetal. Fluids are drawn from the mouth into the tooth. Bacteria, acids and fungi is drawn into the tooth. The pulp chamber becomes inflamed and oxidized. Slowly the enamel surface begins to de-mineralize and salivary enzymes start to break down the tooth and bacteria take hold to further decay.  So yes, what is present in the mouth affects the teeth some, but only as a response to long-term unhealthy digestion leading to malnourished dentinal fluid.  Poor digestion and malnourishment are the originating causes of tooth decay and Ayurveda always proposes solutions to correct problems at their source.  

The key to a healthy flow of dentinal fluid in the proper direction is a nutrient-dense diet rich in minerals and vitamins -- basically a healthy Ayurveda diet.   What you eat is very important because food goes to the stomach and nourished (or not nourished) blood is sent internally to the inner tooth which activates the dentinal fluid.  The coherence of your teeth helps you to grind and break down food which improves digestion.  Good digestion builds stronger teeth.  It's a virtuous cycle.