Mars is 140 million miles away from earth on average. Even if you could detect signals from GPS satellites on earth they would all be at a single point in the sky.
However, that does bring up an interesting idea. Maybe rovers could navigate using the position of the stars? It doesn't require you to launch 4+ GPS satellites into martian orbit.
I don't see why not - automatic celestial nagivation systems are already a thing on earth, you basically have a system that uses a camera to look at the sky and it gives you an accurate position - most military planes use it as backup in case GPS ever goes down.