I tried setting this up to test - my only issue is that I do have a reasonably aggressive power saving settings.
I was able to set up the the avast screensaver but the monitor turning off after 5 minutes, seemed to stop the scan, as it would be considered activity, albeit negative. So when I came back my screen was blank and no screen saver running, bringing the monitor back up would also kill the screensaver scan if it were still running in the background.
The only way was not to have any power saving settings - and the screensaver scanning responded as expected.
I just can't see the point in screen saver scanning, I would much rather have power settings than scanning.
With a resident on-access antivirus like avast, the need for frequent on-demand scans is much depreciated and that would include the screensaver scan. For the most part the on-demand scan is going to be scanning files that would be otherwise be dormant or inert. If they were active files then the on-access file system shield would be scanning them before being created, modified, opened or executed.
I had avast set to do a scheduled weekly Quick scan, set at a time and day that I know the computer will be on. This Quick scan has also been abandoned.