No it doesn't. At least not the bounce rate you're thinking about. (i.e. not the one measured by your stats programs and analytics).

In theory though, some people (including myself) feel that Google does measure a "bounce rate" in the sense of searchers who click a result and then return immediately after to the search results unsatisfied to click on another result.

In contrast, you can have a website with a very high bounce rate (as measured by analytics), and that would be perfectly fine as it may immediately answer the visitors' queries. Examples of that are many informational searches like "What is X".

Bounce is not a very good indicator of website quality for that reason. But don't take it as licence to not work on improving your user metrics like bounce rate, time on site, etc. Putting effort into improving those metrics is a win-win-win for all three parties involved.

As retsek said, if you're just going to think of the number of people click Back after seeing a page in your site in general, it's not going to be a good indicator of your site's quality. Although it might be considered as a factor, you have to think of the fact that you may have presented your information well enough that the people don't have to look around that much anymore.

Bounce rate is a less important metric for a website, whereas, actual bounce rate is an important thing to consider. Search engines can track actual bounce rate of a website and vary SERP ranking of a website.