In my opinion it is not necessary. Remember we only gamma correct to get the math working correctly in the render. If we want a specular color that is blueish, say rgb=27,77,109 then the color is equivalent to hsv=203,0.75,0.43. If you use this as your specular color, with a specular weight=1, then that is the same as using hsv=203,0.75,1.0 with a specular weight of 0.43. If you gamma correct the color, it is like you are actually changing the weight too.
So I do not think you should gamma correct specular weight or color.
– David