Consumer grade GPS actually won't work at 30,000+ feet at speeds the plane would be flying. This is to prevent someone from using the GPS system to steer a ballistic missile.
My cell phone GPS works at cruise on an airplane. I can't attest to how location accurate it is but the altitude and speed are usually right on with what the infotainment system says.
The gps on my phone begs to differ. You can (sometimes) acquire enough gps locks to get a signal and subsequent gps data like speed, position, etc. Worth a shot trying because there's very few other times where you'd be able to see your gps sensor read 600mph. You're probably right though, it's just that the cutoff speed is higher than whatever a commercial jetliner speed is.
They have been relaxed since then, but all current commercial jetliners would stay comfortably within both limits.