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Yes, it matters, a lot.
The Analytics bounce rate isn't directly used though: Google will most likely look at someone searching for a keyword and then clicking a link, followed by how long they roughly stay on that site before making another Google search.
If it's the exact same search within say 30 seconds, that probably means your site isn't so great. If it takes you 10 minutes and you look for something completely different, such as "buy flowers online" followed by the name of a bank to log in to their online backend (perhaps to transfer money or check funds), then that's going to look great for the flower site.
They likely do this over thousands of keyword searches and edit their SERPs accordingly. If a #2 spot on Google has an average 'time before next Google' of 7 minutes, where as the #1 spot has an average 'time before next Google' of 15 seconds, the odds are that these two should be switched.
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