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.

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

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

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.