Well, yes, but that means it also takes a the same amount of energy to thaw. That's the whole idea: large heat capacity to create a temperature buffer.
Sure, there is overhead. But it is not immediately obvious whether or not GP was referring to those particular energy inefficiencies, or the relatively large heat capacity of water.
It is also not immediately obvious whether the losses when freezing ice would be less efficient than energy losses due to the heat produced by charging up a battery, and the leaking of charge. If you take all energy loss into account, the questions of efficiency can have counter-intuitive results[0].