After thinking about this over night I am doubting it would be more efficient.
Warming water that is cold from supply would be good but the warmer the water, the harder it would be. The cold side would be just as bad. Cooling from room temperature would be OK but keeping a cold fridge cold would not be a good place to collect heat to warm the water.
Lastly, the worst case scenario would be a vacation where we need cold in the fridge but don't need hot water. The water would soon reach a temp where it would be very inefficient to cool the fridge.
In a high occupancy building it might work with lots of water usage but a home is not ideal.
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