I find it plausible that Google uses the number of visitors to a website as a ranking factor.
- Google can get this data (See Can Googlebot read any hosting stats?)
- Google Analytics: Although Google has said they won't use Google Analytics data for ranking purposes.
- Google toolbar: The Google toolbar sends data to Google about every page that the user with it installed visits.
- Firefox and Chrome Safe Browsing: Google runs a service that checks the reputation of websites that you visit. It is enabled in both Firefox and Chrome by default and it sends information about each site visited to Google.
- Other PageRank indicators: Other browser plugins that show the pagerank of a page also send the URL to Google for every page visited.
- From ISPs: ISPs often sell data about which pages their users visit. I don't know that Google buys this data, but it could. In the case of Google Fiber, Google is the ISP.
- From DNS servers - Google runs its own popular DNS servers. Users send queries to these Google servers to get the IP addresses of the sites they are going to use.
- Amount of traffic would be correlated with site quality. Google would be especially interested in the number of visitors that are using the site because they want to. Google would certainly want to filter the data. They would do so in a manner similar to how they have to be very careful about which inbound links to count.
- Filter out bot traffic
- Filter out or discount advertising traffic
- Filter out fraudulent traffic
- Filter out traffic that Google itself sends the site (to avoid a feedback loop)
Even if Google does use traffic as a ranking signal, it would probably be a minor one.
- Most of the time amount of traffic would line up with other indicators such as Pagerank
- Google has never announced that they use any traffic signals as a ranking factor
The reason for Google to include traffic as a ranking signal would be to catch sites that suddenly get lots of users and a good reputation without using SEO as their primary traffic source. Sites that go viral or rely on social media for example.