i was wondering if the avast screensaver runs a virus check if u are already running a system scan in the actual avast program. its not really neccessary to have two antivirus checks at the same time now is it? 
Not sure if it does run, I think it is but others will tell you.
Anyway I always close the on-access scanner when running a system scan 
If you run a system scan it’s better to turn off your screen saver.
A little but very efficient and fast way is the program QkSav2k 2.06 (Screensaver Control Powertoy) 
On contrary, I do not turn off the on-access scan. I understand what Artras posted but I will forget to turn it on after
If you let the screen saver start and the avast screen saver module in your screen saver, you will be scanning twice: system + screen saver and, if you want, the third will be on-access… Well, it’s not necessary, time consuming and useless 8)