No.
Oh, alright, you want more? Well, the claim that a page’s ‘bounce rate’ affects search engine ranking has been around forever. I’ve probably even wondered here on this blog if it was the case. But if you think about it, the measurement (the percentage of people who entered a site on a particular page and then left the site from there) is very questionable in isolation. Just this week, I got 700 people to click through to a blog post. I made no effort to keep them on the site, and nearly all left after reading the article. Technically this was a 100% bounce rate, according to Google’s definition. But the search engine doesn’t know whether the page did its job, which in this case (if the visitors read the piece) it certainly did.
What ‘bounce rate’ may be useful for is to compare types of pages, or designs. If I added something attractive at the end of the article which caused most readers to click on it, that would change the bounce rate considerably. So if our inputs are consistent, it can be a useful design analysis metric. And if our goal is to make our site more ‘sticky’, it’s a good thing to monitor. Otherwise, I never include it in analytics reports.