I'm just about to try G+ on my site, but a friend reports her site jumped a page in the search ranking for her main keyword in about a week.
The +1 button shows a correllation with traffic only because the more traffic your site receives, the more likely you are to get +1's. In my opinion, the +1 button does not have a big effect on SEO at the moment, however as more and more sites start using it, I believe google will start using it to see trends on the web. Just my personal opinion.