Yes! I've seen people with some very striking white teeth in India which is a place where people often do have horrible teeth (often from betel nut use). So the twig users sometimes really stand out. The Wikipedia article has a good point about frequent use though - some people clean their teeth with these twigs almost like a nervous habit and are very intense about it.

What the article doesn't mention is the salivation that Neem twigs cause! Neem trees also produce a biocide called azadirachtin and although the concentration is low in twigs maybe it helps clean the teeth when used a lot?

I used a Neem based shampoo for a short period, but my wife complained that it had an atrocious smell. Guess Neem based oral hygiene would take this to the next level...

Just make sure to identify the plant first, and ensure it is suited for that (unlike the poison oak twig which the naïve city kid picked on one training deployment when trying to impress the country rubes with his knowledge of woodcraft --- fortunately a medic was able to perform a tracheotomy when the allergic reaction swelled his windpipe shut).

My grandmother was hospitalized, as a child, after she ate a hotdog she roasted on a poison oak stem.