No. "Logging in" is handled by browser cookies, files stored on the individual computer(s) in question. That is, whether you're logged in or not, and as whom, is information stored locally on that computer's hard drive. If you don't want to stay logged in on that computer, you'll have to remember to log out on it before you leave.
OTOH, there's no harm to staying logged in. It has no effect when you don't have the boards open on that computer. So, if you leave yourself logged in on your friends' computers, nothing will happen unless they choose to come to the boards. In that case, they could post as you, if they wanted to, but what kind of friends would they be if they did that?
Paul