On the object side, that's true, though of course the magnification will change. On the image side, though, it isn't true unless the image sensor is butted up against the output facet of the GRIN element.
Most modern endoscopes are GRIN-based, because GRINs don't exhibit the buildup of field curvature characteristic of cascaded sets of relay lenses.
I don't know how (or even if) they control chromatic aberration.
Cheers
Phil Hobbs