I am beginning to believe this is a dangerously misleading analogy because what we describe as energy in productivity terms is definitely not a resource that is depleted and refilled, but something that behaves very differently.
For example, lets say you are in a productivity slump but then a few nice words from customer turns it all around, you feel full of energy and motivation and crush your work with enthusiasm. The customer has not handed over a resource, instead, their words have changed ideas in your head. The ideas in your head are dictating whether you feel full of energy or in a slump, not a quantity that follows the rules of conservation.
An example of a different analogy that conflicts with the battery version is to describe energy/motivation as a fly-wheel. If your don't put enough energy in, it will stall and all energy you put in is lost. However get it up to speed and it can be self-sustaining - you seem to get more out of it than you put in. I find that more interesting than the battery but its also pretty weak.
Addressing the true causes of productivity requires understanding how our thoughts lead to feelings of energy and motivation. The battery analogy is tempting because it is easy to understand and makes the problem seem tractable but its actually disguising and hiding the hard problem.