Curiosity got me so I googled significantly... and find no mention of a relationship. In fact to the contrary I find use of baking soda and/or peroxide suggested to cancer patients for various reasons: cancer baking soda peroxide mouth cancer - Google Search
HI,
I do know that brushing with hydrogen peroxide can help with gingivitis, as my Dentist recommended it years ago. It did help, along with the work he did to rid it.
Best of luck.