In a 1 bit environment (==single SSID visible), sure. But most of the time multiple SSIDs are visible, and correlate to each, making detection of abnormalities easier. And the lat/long is also visible to help disambiguate.

I think OP meant the opposite issue of broadcasting "I live at 123 evergreen terrace" everywhere you go, because SSIDs are vaguely unique.

Would both the stationary and mobile instances of that SSID be visible on public databases like https://wigle.net?

You’ve reminded me of a project I started and never got it working. A home network on a vpn to another location.

So the usually ssid is in my home country, and another ssid is based somewhere else geographically.