No, how much traffic a website gets, does NOT influence ranking.
If it did, everyone would be on Fiverr, buying fake traffic... or selling it for "top rankings" lol.
That's why some marketers are able to make the bulk of their money through product launches and stuff.
Some marketers make the bulk of their money through product launches because they have an email list, or affiliates that have an email list. It has nothing to do with ranking in Google though. In fact, I've seen some marketers that have garbage SEO but they still make money because SEO is not part of their traffic strategy.