there is plenty of data about the subject.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2906228/
https://www.mchoralhealth.org/PDFs/OHHomelessfactsheet.pdf
more with a simple google query like 'oral health among homeless'.
overall point : homeless people are less likely to have a 'dental home', or access to the items and services needed to facilitate good oral health.
The problems of access seem to correlate to an increase in oral-health-related issues like sensitive teeth, broken teeth, and ulcers.
It's not a fashionable subject, and it's tough to say in such a way that is sensitive to those people who are undergoing such strife, but the data tends to point towards worse oral health in those without access -- which, in my opinion, is an obvious outcome of destitution and homelessness.
How do you feel about saying "if a black person (or any individual) were to bite you..."?
From the perspective of sepsis the oral health of the person has no impact on how dangerous a bite is. Every human being has enough bacteria in their mouth to cause a deadly infection and having a higher level is not significant.
The original poster mentioned the homeless because that's what he thinks of when the idea of unclean mouths comes up.