Mantra, as you know, by default avast! checks if there is an available connection each 40 seconds. If there isn't, wait more 40 seconds to check. If there is a connection, check for an update. If there is not any new file to download, wait 4 hours to start checking again. If there is an available update, start it and install it. Again, wait 4 hours to check the next time.
I think you can check the dial-up option, that will check only when the 'connection' is detected.