That would be a cool trick. I think it will be a long long time before we see that.
GPS, and GLONASS have 24 satellites for global coverage. Galileo has 27. Beidou has 10 right now, but has limited coverage. It will have 35 when it's fully operational.
Most (all?) require ground stations to keep them updated, so it isn't just a matter of throwing some satellites up and having GPS on another planet. As I recall, GPS satellite service will degrade to unusable somewhere between 90 to 180 days. [insert obligatory apocalypse reference]
Theoretically with GPS, you can lock with 3, but that assumes a highly clock on the receiver. Our phones and GPS receivers aren't that accurate, so we require 4 satellites.
But I believe this was dumbed down for the casual reader, so they said "GPS". Using the known location of the orbital vehicle, gravitational center of mars, magnetic poles, and stars optically with a sextant, and using inertial sensors, they could put it down on a precise target.
They might use GPS for test flights here, since we have the luxury on this rock. They aren't accounting for other things with their tests right now. Like the Mars average ground level air pressure is 0.087psi. The summit of Mount Everest is 4.89psi. The highest surface air pressure they'll get on Marswould be Hellas Planitia at 0.168psi.
They're going to need some *huge* propellers on their quadcopter. Flying on Mars is like flying at just over 100,000 feet on Earth. The record for any propeller aircraft is the Boeing Condor UAV with no payload, at 67,028 feet.
The record altitude for a helicopter in Earth's atmosphere is 40,820 feet, and it also got the record for the longest autorotation when the helicopter stopped flying. :)
But other than navigation, and lack of atmospheric pressure, it could work fine. :)