Interesting question. And I would agree with the previous posts.
Since the rate of climb in a steady state established climb is directly related to the excess thrust being produced over that required for the same airspeed in level flight it would follow that by reducing the induced drag, (by moving cg as far aft as possible and thereby reducing the total lift required and hence the induced drag) you would have less total drag and therefore greater excess thrust available, which would translate directly into a greater rate of climb.
As a side note I can recall a vector diagram that demonstrated that the total lift being produced by the wings in a climb is less than in a power off glide.