Do you mean you don't have anyone logged into AC, or you don't have anyone logged into the computer running Amazing Automator? If the latter then I'll see if I can figure out the problem.
You are correct, AC does not need to be running for the Backup to work. As Bert observed, Automated Backup sits in the service tray area.
When I used Win XP Pro or Win 7 Pro on my main computer, I never tried logging out when I left at night. I used "change user" to switch the computer to the login screen. Backup worked automatically, but sometimes I had to reset the Automated Backup option if I rebooted the computer (the Automator wouldn't appear in the system tray after restart).
I now have Windows Server 2008/R2 running on the main computer. The Automated Backup works even if I don't log in as Administrator. It also always resets correctly even if I need to restart the server. I suppose this has something to do with the server software, as Bert was explaining.