I am running Windows 98 and have a 233MHz, 224 MB processor.
Before defragmenting, I stopped all programs I could including Avast from the System Tray (Stop On-Access Protection and Exit). Still Avast appeared to be doing something. Only when I remove Avast from the Autostart list and reboot it seems to be really inactive.

Also, as mentioned, when enabled, Avast tries to access the internet in the ‘manual update’ mode as soon as I dial up.