Yes, and this is obvious when you think about it. Sugar causes both inflammation (actually any carbohydrate will eventually) and sugar is why you brush your teeth.

Fascinating books on this include "pure, white and deadly" and "cancer: disease of civilization" (this one is hard to find, written in 1962 I think). The former was written before sugar fully took over, the latter was written back when some cultures didn't get cancer.

Not surprising if true. It seems swallowing the bacteria that flourish when you don't brush/floss your teeth leads to damage to your heart valves (wild!) so other immune responses, typically leading to inflammation, are quite likely.