I don't think using Google Analytics will help in improving a site's PR. As mentioned above, it's just a stats program. PR is about incoming links to a site.
They wouldn't offer an incentive that would harm the integrity of their results. PageRank is based completely on backlinks, there are no other contributing factors.
PageRank is just one of many factors determining your placement on the search engines, but Google Analytics won't improve your placement at all.
It's been said again and again in this thread but I'll reiterate. High quality links improve PR. Full Stop. Sitemaps can help with indexing. That is their only real function.