Sounds interesting, indeed. Just dug up this review [1] that claims there were no adverse effects from any of the interventions, and that after 2.5 to 3 years of use, a fluoride toothpaste containing 10% xylitol may reduce caries by 13% when compared to a fluoride-only toothpaste.

I wonder how well bacteria will adapt long term in your mouth to Xylitol exposure through bubble gum based adminstration.

[1] Xylitol-containing products for preventing dental caries in children and adults. Cochrane Database of Systematic Reviews 2015, Issue 3. Art. No.: CD010743. DOI: 10.1002/14651858.CD010743.pub2.