With the GBA, the original GBA screen and the first gen GBA SP had very washed out colors and not saturated at all. The Mario ports to the GBA looked doubly since they desaturated their colors and were shown on a desaturated screen. I've heard that the real reason the colors were desaturated was because the first GBA model didn't have a backlight so the colors were lightened to be more visible, but I'm not quite sure that's the case. Lots of other games didn't do that.

And with the second version of the GBA SP and the GB Micro, colors were very saturated. Particularly on the SP. If anything, cranking up the saturation on an emulator would get you closer to how things looked on those models, while heavily desaturating would get you closer to the look on earlier models.