Filling the fridge or freezer volume with items heavier than air to reduce the energy draw is a myth. Cold air moving out and warm air moving in has very little effect because the volumetric heat capacity of water is 4,000 times higher than that of air. In other words, to change the temperature of 1 cu.ft water by 1 degree takes 4,000 times more energy than of 1 cu.ft of air. And it costs even more to go through phase transition, i.e. turn water into ice.
And then you have to continue spending more to keep this ice mass frozen, because the higher is the heat capacity and the higher is the difference between the inside and outside temperature, the more energy you need.
To reduce the energy draw, you have to either reduce the temperature difference or reduce the volume. One way to reduce the volume is to fill it with foam peanuts in ziplock bags, though I wouldn't bother because the savings on cooling less air are insignificant.