I hate to rain on your parade, because I'm deeply interested in alternatives for established models, and as a rule I strongly prefer intuitive visualisations over mathematical wankery, but this is just... nonsense.

It has nothing to do with electricity in any sense. There's no matching theory that this is visualising.

To begin with:

1) This doesn't explain why in general only metals conduct electricity. You used the example of Hydrogen, which is a nonconductive gas. It might become metallic under certain circumstances, but nobody has a firm grasp on exactly how that works! Using the conditions found only in the cores of giant planets for a "simplified" example is absurd.

2) This doesn't explain why capacitors build up charge (literal excess electrons on one plate, and missing electrons on the other plate.) That is, your theory inside the wires has to also mesh well (heh) with what happens outside the wires, such as the buildup of static electricity.

3) It doesn't explain how electrons conduct electricity through the vacuum, where there are no atomic orbitals.

4) It doesn't explain how rarefied plasmas conduct electricity, where for the majority of the time atomic orbitals are not in contact.

5) It doesn't explain other types of current, such as charged fundamental particles in cyclotrons.

6) You haven't explained how batteries produce the rotations.

7) You haven't explained how dynamos produce the rotations.

8) You haven't explained how resistors, capacitors, and inductors work in this model.

9) You haven't explained how the rotations produce heat, light, or any other useful work done by with electric machines or with electronic devices.

10) You said that ionised hydrogen atoms are required for this to work! But they are just isolated protons. They have no electrons or electron shells!

11) This is actually a flaw of other models too, but I'll throw it on the pile: The infinite extent of the QM electron field is just a simplification of the QM mathematical model. Clearly, this is physical nonsense. A hydrogen atom can never have an electron orbiting it meters away, or light years away. That's just gibberish.

12) And the final nail in the coffin: You'll find that in general an extended 2D or 3D grid of gears will often get "locked up" and cannot transmit rotations. This is practically a meme at this point: https://www.reddit.com/r/CrappyDesign/comments/2hwwy0/those_...

For comparison, the liquid flow model is actually relatively accurate in terms of representing what's really going on (electron fluid flowing freely), and is also intuitive.

1) Resistors are like an constriction of the pipe. Flow is allowed but impeded.

2) Capacitors are like a wide section of the pipe, but blocked by a rubber sheet. Bulk flow through a capacitor is not possible, but vibrations can be transmitted.

3) Inductors are like a heavy propeller in the flow. The propeller resists flow while it's being "spun up", but then it no longer resists the flow when its speed matches the flow. If the flow in the pipe is reduced the momentum of the propeller provides pressure to keep the liquid flowing longer than it would have otherwise.

4) Transistors are like a soft rubber section of an otherwise inflexible pipe surrounded by a container with an input. Pressure in the container squeezes the flexible section and prevents flow through the pipe.

Etc...