There are two ways to think about this, 1st generation and 2nd generation.
First Generation Impact:
Google keeps records of all search histories and the links, on Google search pages, that people click on. Theoretically Google could use this information to assist in the ranking of pages.
Does Google use click rates as a ranking factor? This is exactly the type of thing that Google is so good at keeping silent about. No one knows. Traditionally, most SEOs have sworn vehemently that Google does not use click rates to help rank pages. Over time though, confidence about this has lessened.
If they do it is probably weighted quite low compared to other ranking factors because the number of clicks that a link receives is largely determined by the document’s existing position in the SERPs. In Excel terms this would be called a ‘circular reference.’ As you know, a circular reference in Excel results in an error.
What does make sense for a search engine is to investigate anomalies and the only reason I can think of why click rate might become a factor is if a listing’s click rate becomes anomalous, either above or below the norm. If this becomes the case Google might do something algorithmically like spider the web site more deeply to see if there are additional ranking factors that should influence a document’s position in the SERPs. I deeply doubt the any impact would be direct.
Second Generation Impact:
If you have read Malcolm Gladwell’s The Tipping Point this will make sense to you. After a web document reaches a certain level of links and traffic the natural traffic and links to that page will continue to increase, separate from any marketing effort (though not forever). On the Internet word of mouth is typically accompanied by links and because some of those links will be on blogs, forums and other web pages they will be counted by Google and add to the ranking strength of the given web document. If that natural increase in strength outpaces its higher ranking competitors the document may rise in the SERPs.
In a real world example, one web document that I built and marketed received X number of links for via direct effort. Through my efforts I was able to get it on the first page for several three word key phrases and the third page for some very popular two-word search queries. That document now has over 3X number of links, two-thirds as a result of natural linking without any effort on my part. It has several first page rankings for popular two word searches, rankings that floated up from the third page. The number of links continues to increase and so does the document’s traffic and Google rankings.
FYI, I used X instead of the actual number because X is scalable. The tipping point for any page depends on interest, quality and competition.
I should also point out that that document does not look the same as it did in its original incarnation. Over time I have tweaked and updated it and re-targeted the page’s on-page optimization. What is important though is that every change I make is designed to take advantage of increased ranking potential that is being created by new naturally occurring links and to keep the content fresh and interesting so that word of mouth links continue to increase.