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.
They have been relaxed since then, but all current commercial jetliners would stay comfortably within both limits.
Incidentally, my GPS watch (Garmin) was working last time I was on a plane. It was bang on 700kph the whole time IIRC.