http://www.google.com/intl/en/analytics/privacyoverview.html
http://support.google.com/analytics/bin/answer.py?hl=en&answer=1011397
According to the GA privacy statement (first link) and, more specifically, their data sharing policy (2nd link), Google would be in direct violation of their own policies if they used your data to improve their search product, provided you have the "Do Not Share my Google Analytics Data" option set.
Do not share my Google Analytics data: This option excludes data from being included in any automated processes that aren’t specifically related to operating and improving Google Analytics or protecting the security and integrity of the data.
Google employees have said before that their is absolutely no link between this data and their search algorithm, though "saying" that isn't as iron clad as the above sharing setting.
Of course, Google's recently found a few ways to violate privacy, so anything can happen. Their publicly available privacy policy is the best we can do!