In any way could the body store electricity supplied externally?
No, the human body cannot utilize externally applied electricity. Applying electricity to the body will either have no effect, if the amount is small, or will disrupt normal functions of the body or cause injury if the amount is larger.
An overview of the effects of electricity (for doctors) can be found in "Conduction of Electrical Current to and Through the Human Body: A Review".
Not to be a smartass, but do you not consider the mitochondrial electron transport chain to already sort of do that? When we consider that actual movement of electrons to be a step in the conversion of chemical potential in fatty acids and carbohydrates to phosphorylating ADP for later mechanical energy. Just a thought.
Although I'm assuming you mean somehow utilizing a current flow through the body from an outside source.