Since it is clear from the source in your question that melanin can absorb energy from gamma rays, yes higher concentrations of it would reduce the energy of gamma rays getting through the skin. However this would not provide any real relative protection, the gamma rays are still going to go right through your skin and start damaging DNA.
Gamma rays are three orders of magnitude higher frequency and therefore carry much more energy than UV. Of course there are energy transfer inefficiencies but since the fungus are not growing at even an order of magnitude faster, it's fair to say that melanin is not absorbing all of the energy in a gamma ray.
Since the gamma rays are not fully absorbed by melanin, they will still go through the skin and will still be able to do significant DNA damage.
So yes, but not enough to really matter.