I have been using Avast on my laptop since my NAV subscription ran out at the end of May. Set it up and very impressed with it so far. The scan you refer to is at boot up and as you say looks like a DOS screen which it probably is. To cancel it and proceed to Windows boot you press ESC key. I have never seen it run on the laptop so it is a setting somewhere.
I put Avast on another machine last night. (Very bad case of Adware, virus`s etc) Because I didn`t want to connect to the internet I loaded it from disc and skipped the registration on line. When I rebooted the scan you refer to appeared! A little more "ferreting" and I realise I must have selected a scheduled Boot Scan.
To do this open Avast and right click the vertical bar on the far right of the interface. A host of options come up - Incidentally if you do this whilst a scan is in progress you get options for background scans - select "Schedule Boot Scan" and you are asked to reboot your computer. Voila!