I am relatively new at this, so forgive a potentially dah! question.
I am convinced that traffic is one of the variables in search engine's establishment and maintenance of page position, along with the god - Links.
Here's my question. Does traffic that comes to your site from Adwords count as traffic and hence help build your organic position. It seems to me that someone like Google would want to count that since they are trying to establish "real relevance". Whether traffic comes through organic clicks or through Adwords, its an indicator of relevance.
Now that's my reasoning BUT, what does experience say?
"...Does traffic that comes to your site from Adwords count as traffic and hence help build your organic position..." Sure it's traffic, paid traffic but still counts as traffic but it isn't suppose to help the webpages in the organic results. Does it help? Maybe, maybe not.
I would suspect that the search engine, as it gathers up all kinds of different information about the webpage in order to develop a ranking for it when a particular keyphrase is used in a search, probably considers the choices of keyphrase bids associated with a webpage and makes some sort of comparison with what it discovers from a normal crawl. Does this translate to increasing merit to a webpage? It's not likely but I would imagine that the search engine would get quite confused when both factors don't jive; perhaps to the point of non-rewarding the webpage with some kind of damper rather than actually penalizing or demeriting the web page.
If you are making more money by using Adwords with an SEO campaign then it makes sense. Running Adwords will not affect you SEO work postiviely or negatively so do not let that be a factor in whether you do it or not.
Traffic does not have a direct affect on seo ranking. A website that gets more traffic from any source will eventually rank better because people tend to link to pages they like and the more people that visit your site the more people that will link to you. A lot of amateur seo's look at a few SERP's and come up with all kinds of wild ideas about how Google ranks websites. It is all about links and quality of links.