Well I'm on dial-up and my connection doesn't grind to a halt whilst updates are going on.
What you want to do is what I do and delay the update check, I have mine set to delay by 10 minutes (600 seconds) so I can jump on-line do something quickly and get off.
You need to edit (using notepad) the [InetWD] section of the C:\Program Files\Alwil Software\Avast4\Data\avast4.ini file and add the following line (depending on your connection type enter one or other of the Bold lines below):
Dial-up connections, add this line:
RASWaitSeconds=600 and
UseRAS=1 if not present (or edit UseRAS=0 to UseRAS=1)
[InetWD]
UseRAS=1
RASWaitSeconds=600
When complete save the changes, avast's self-defence module will ask for confirmation, etc. answer Yes.
The figure is seconds and the above equates to ten minutes, you could try that and adjust upwards or downwards if required.