GPS uses time delay differences to determine position, similar to LORAN and other so-called hyperbolic systems, the 2d locus of points of equal delay formed in 3d space forms a surface on which the receiver must be located, the intersection of several surfaces from multiple satellites gives an accurate fix in three dimensions. I'm pretty sure you can use GPS to locate a spacecraft precisely in near-earth space, but you would probably need specially engineered recievers and software to calculate your position. I don't think the system could handle large distances (several times the height of the satellites above ground), because it wqs never designed to do that, and because the signal strength would probably not be detectable at distances exceeding several earth radii. Near the moon, for example, the spacecraft would not be scattered about the sky, they would all appear to be cluttered around the earth. The equal-delay surfaces would be flat planes and the slightest imprecision would cause the intersection lines to shift around enormously.

Even with Lines Of Position used in visual navigation on the water, the quality of the fix improves enormously if the LOPs are at right angles, to minimize the effect of imprecision in measurement. If bearings are taken of objects only a few degrees apart, even the slightest imprecision in the measurement causes the intersection point to move enormously and the fix is not trustworthy.