I watched it for several days. The max I ever saw was 5% use, though mostly 1-2% as opposed to system, browser, Android, etc which use more. 5% was when I scanned over 10000 files internal and external card and that is a heavy duty job when you think about it. Otherwise zilch here.
Edit:
My numbers are from Toshiba Thrive, I forgot to say it.
Also, I hardly ever see Avast in the battery use statistics - on and off it is mostly 0-1%, sometimes 2%, and I see no impact that I could feel. Network meter is running here.