Nay.. none that I have seen anyways. I don't see why they would take something like your quality score (relevant keywords in ad + landing page kw + ctr,etc) in order to rank your site organically.
Hello, There are a few rumours going approximately that becoming an AdSense applicant can assist your site in the ranking but nothing definite has been proved yet.
Adwords does not directly affect ranking. However, it may affect it indirectly. Adwords can be used to draw traffic to your website and when people get to know of your site and they see that it is very helpful to them, they will bookmark and make references to your website on the internet, giving you free backlinks. Hence, high search engine ranking.
When I browsed the forum I found this question was asked here several times already. There is no connection between the two. Rankings can be improved only with good content and quality backlinks.