Does beer color change with efficiency?

Does the color of your beer change with the efficiency of your mash?

I would say yes, but I think the difference would be nominal. I doubt you'd see much of a difference in color even with say, a 5-10 point difference.

Only if you expect 80% and get much lower. You won't have as much fermentable wort so the color will be lighter. If you compensate for your efficiency there will be no change. For instance, I have efficiency problems myself that I'm working on. When I brew someone else's recipe that calls for 75-80% efficiency, I scale the recipe to match my 65% or so. In the end what you get in your boil kettle is the same.

Wouldnt it be richer in color depending on what grains were used?

Color is largely driven by the specialty grains and mash time. The tie-in with efficiency would be more a matter of sparging and how well the grains are washed.