if so, is there a problem with the practicality of this where one equals the other?
So, you can conceive of no practicality problems with getting exactly the same amount of energy out that you put in? Like
Corribus: said, there are always losses in transport and and transmission, so you want to ignore that, for the time being? Sure ... but why? What's the next point in the discussion? Maybe you'd like to use electrolysis as an energy storage medium? That is, perform electrolysis when energy is plentiful (i.e. solar cells in the daytime) and burn hydrogen when you need energy (to continue the example, at night.) I suppose that's plauible, but since there are always some losses to side reactions, and wasted energy, why discount it, even for an academic question?