Thanks for the answer. But couldn't you test it by setting up two very similar websites (not identical because you'd presumably get penalized for duplicating content), in which one uses Google Analytics and the other doesn't, and then watch the ranking over time. If the analytics site does significantly better than the other, that would strongly indicate that Google gives it preference.
It would be a decent undertaking to build two websites with comparable but different content to test search rank. It is also very probably that the search ranking algorithm is nondeterministic.
