I believe Matt Cutts already stated that they don't use any click stream signals from their toolbar in their rankings. So much has been said about this that I haven't been able to find the quote. I may have even gotten wrong which Google employee said it.
He said they don't use Google Analytics data. He has also said that the toolbar doesn't affect the indexing of a page. I don't see anything about the toolbar affecting rankings though.
Hmm... I don't think that's what I was thinking of. The wording was very specific. I don't recall Google Analytics being part of the comment, but of course I could be mistaken.
The 'privacy' link from Analytics leads back to the general privacy pages, and their overall privacy policy says Google may use any information they have (from logs, cookies, etc.) to "[p]rovide, maintain, protect, and improve our services (including advertising services) and develop new services".
