In avast! 4 if you’re on dial-up you can configure the .ini file to ping your modem instead of the server when checking for updates. Anyone know if the same setting should work in avast! 5? [InetWD] UseRAS=1
Thanks! 
Have you set the Settings, Updates, Update Parameters to I only connect to the internet using a dial up modem ?
See image, that is my setting and I believe that stops it from pinging the server.
However, that said, if you open the GUI before you have established a connection, it will try to connect (it does on mine). As far as I’m aware this is to populate the ad information of the day, etc. in the Summary section of the GUI.