Perhaps.... but Google would still know your real location, no?

And your carrier, and anyone who does location based on IP, and anyone who does location based on inaudable noises only your phone can hear (https://arstechnica.com/tech-policy/2015/11/beware-of-ads-th...), and...

But, this would still help protect against the simplest way to steal your location data, which is what a lot of services do

There's a hardware switch for the mic but yeah it's pretty hopeless to hide your location in those threat models.