By logging off you will close your session on the server. It could be that if we all did it we would get a quicker system but its unlikely. The server will no doubt clear sessions after a period of time to prevent there being lots of non-closed one's clogging things up.
Some secure systems force you to log off, or if you don't log off before closing the browser window will lock you out or prompt you next time to log off first.
This isn't a secure site so there is no security risk involved.