What exactly do you mean by hiding the icon and which icon are you talking about ?
If you are talking about hiding (windows taskbar) or not displaying (avast settings) the avast tray icon, that wouldn't stop update notifications as the avastUI.exe would be running but not displaying the icon. This has been the same for as long as I have been using avast (4.x to 8.0) just over nine years.
You can disable the auto update notifications (nothing to do with the tray icon) avastUI > Settings > Updates > Details, uncheck the 'Show notification box after automatic update' option.