It is now confirmed that all the desktops CAN UPDATE through the proxy after I applied / enabled “My computer is permanently connected to the Internet.”
I feel relieved… 
Anyway, why does this condition is not mentioned in the manual / documentation? ( Or I miss it somewhere ? )
When direct connection ( which is the default ) is used, there is no need to enable this option, but when we choose other connection options, this option must be enabled in other Avast to update its definition regularly.
For some people ( like me ) this option seems to be related with the dial-up connection thing. To force Avast to check for updates regardless if the connection is dial-up.
When behind a proxy, of course, assuming that we have no idea to what kind of connection the proxy server is using, it’s wise to assume that the proxy server is not always connected to the internet or there is a possibility that the proxy server will refuse any connection attempts for some reasons.
Anyway, thanks for providing an excellent free antivirus solution.