Impossible… avast does not have a dialer and/or a connection handler.
Autoupdates of avast! only are done when you are already on-line. It searches each 40 seconds for a connection and, if succeed, wait 4 hours to the next tentative.
Only if you’re on-line avast! will try to connect.
You seem to be infected with a dialer. Did you run SpyBot or Ad-aware to be sure?