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?