Surely if you have a program that you don't want to 'start,' 'update' or connect to the internet, what is the point in having it. Surely that is a candidate for uninstalling.
It would be possible to prevent it connecting to the internet if you have a firewall with outbound protection, in which case you should be able to block its executable from connecting.
You don't say what avast version you have, only the AIS and Premier versions of avast has a firewall.