Anybody using Avast Antivirus: Does the screensaver that comes with it actually scans the computer f

Yes it does

"A special screen-saver is also provided, that, when running, performs virus scanning. avast! antivirus works together with your favorite screen-saver, so you don't have to change your personal settings to use it."

right click desktop%26gt;properties

%26gt;screensaver%26gt;avast antivirus

click on settings%26gt;screensaver

here you can actually select any screensaver you want

and specify which hard disks you want scanned.