I've tried using Google device location, which uses mobile data, and that works even if the screen is off and locked.
Locating using the Avast website and mobile data is not reliable, and doesn't seem to work at all if the screen is off. Much of the time it seems unable to locate the device, and says anti-theft is off, when it isn't.
I've also tried using another SMS locator app. It works even if the screen is locked.
So whatever future there is for the avast anti-theft feature, there is work to be done.