[TeMPOraL]

No.

First of all, they would need an absurdly large directional antenna to even receive GPS satellites. GPS signals are already below the noise floor on Earth's surface, and we use mathematical trickery to extract them from the background. Secondly, even that would only be possible when Earth's over the horizon at the location of the probe. Thirdly, the whole span of GPS satellites as viewed from Mars would be a small fraction of arc second, i.e. basically all coming from the one place. Lastly, there's extra light lag that you have to compensate for, that depends on relative position and orientation of Earth and Mars.

No, GPS is not suited for use in space, especially not far away from Earth. However, I read once that some Earth orbit missions did in fact look / make use of the GPS signals, as in (low) Earth orbit, they're actually easier to receive than on the ground.

[rz2k]

The third point can be misinterpreted to make it sound like gps involves a steady tone generated from a known location like more traditional navigation aids used in aviation, rather than clocks taking advantage of our understanding relativistic effects.

While Earth is in the Martian sky, and if the signal were strong enough, a viewer could average receiving signals from over half of the constellation rather than only half a dozen. Furthermore the time signals would originate from many of the satellites moving less orthogonally to the viewer and instead moving toward and away from the viewer.

Compared to measuring the sun relative to a changing horizon, it seems plausible that an extremely precise direction and altitude relative to Earth could give even more precise location on Mars.