indirectly having Adsense on your site might affect rankings.
Many people who run Adsense start to optimise their pages on a contextual basis so that the theme of the page becomes entirely evident. Themed vocabulary, contextual keywords, stemming, use of headings with keywords in etc.
In doing this they also start to SEO their pages by making them more spiderable and contextualising them much better.
G are also supposed to be using information from the mediabot for their greater crawl as well as the various googlebots - so again indirectly Adsense on your pages might get you spidered.
Incidentally one of my sites was losing pages recently - going supplemental etc, went down to hompage only.
I don't run adsense on the site but I ran the Google adsense preview tool against each page a couple of times till they showed ads. Pages came back into the index the following day - I actually believe this is purely coincidental but who knows... (fixed typo)
I don't think there is any relationship between adsense and ranking too, at least none that i have seen. But then sometimes you think, wouldn't G make more if sites with higher adsense conversion/better performance get more traffic rather than sending that traffic to sites with the same content quality/relevancy to the particular query but less adsense conversion?
Sites with AdSense might not get backlinks from good authority sites so indirectly AdSense is affecting the search ranking.
I doubt if that's a significant factor. No good authority site will retain that adjective for long if it ignores sites just because they run AdSense ads. For that matter, a large number of "good authority sites" run AdSense ads themselves.