Being connected to the Internet when you are infected can complicate matters as the virus can be trying to gain access to the Internet, establishing a back-door for future use, etc.
This warning (I have never seen it) is advice, I'm reasonably sure that avast will still action the task you select 'Move to chest,' 'Delete,' etc. once you click the button, regardless of your connection.
The advice to disconnect would be my second action to selecting what to do with the virus.