You've got to be kidding. Due to hydrogen embrittlement and fire risk from leaks there's no safe way to push hydrogen around in an underground pipeline network. The closest we can get is distributing natural gas and then converting that to hydrogen near the point of demand, which still requires a lot of electricity.
"Push" includes transport in tanks ... something that happens today. And if vehicles are going to be running on hydrogen, they are going to be transporting it in tanks too. Just like gas stations today, the hydrogen will be transported from the plant to the stations somehow. That movement of energy, as opposed to pushing electricity over wires, would reduce the need for grids as opposed to electric cars which will increase the need for grids.
I would assume that it's just simpler to synthesize methane (power-to-gas) and use that to (e.g.) fuel vehicles. Assuming you're pulling H from water and CO2 from the air, the methane is carbon neutral, so there's no huge reason to try to transport hydrogen.
