I don’t know if propane is different then natural gas, but my natural gas water heater has no electrical connection to it at all. I just put a new one in on May 8th of this year and only hooked up water, gas line and the vent.
The kitchen range is hooked to electricity, but it’s only used for the timer / clock and piezo lighters. It will still work with no electricity if you light it with a match.
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You can run, but you'll only die tired.