The Terms of Service (TOS) for Google Analytics basically say that they can do whatever they want with the data they collect from your sites and this includes using that information to determine search engine rankings.
By installing the Google Analytics code on your site, you are giving Google a back door window into your traffic patterns and they will quickly determine that your (affiliate) site is not the kind of site they want in their index. You see, Google doesn’t really like affiliate sites. Perhaps I should qualify that assertion a bit more. Google doesn’t like little-guy affiliate sites; they don’t seem to have a problem with the big guys and large corporations running affiliate ads on their sites.






