There's this thing called a fan that's inside your furnace. If the electricity goes out - you're gonna die of cold anyway because there's no way to move the heat from the furnace through your ductwork.
But duh, I am realizing that shorting the contact won’t do anything so you’re right.
But I have a small solar generator and could probably make it work from that, because it requires very little electricity, as opposed to say, a heat pump.
Gas valve and igniter run on low voltage, I think the combustion blower runs on 120 VAC, the main blower that distributes the heat to the rest of the house is definitely 120 VAC. A small gas generator that can provide maybe a kW would probably be the most straightforward backup.
Still won't work. If your home is sufficiently air-tight so that you won't die of cold with that paltry amount of gas, you're going to die from the carbon monoxide from your stove.
The propane heater from Home Depot either has the same problem or it uses electricity for the air induction system.
If your goal is to be prepared, a generator and a heat pump will last longer, it will be cheaper for you and society in the long run, it will have more utility, and we have far more gasoline stockpiled and ready for emergencies than we have natural gas.
You can take hot showers with a tankless Propane water heater as well assuming there's water pressure, costing < $300 on the low end. Sure, proper ventilation is important...
Gas spoils & does not store for very long. Diesel & propane are both better at storage.
You can even run generators off propane, though at less power than gas. There's even dual fuel (Gas & Propane) generators you can purchase for < $300 USD. It won't power your house, but it will at least be something which can charge batteries & run small appliances. They are loud though. If you own a house, getting a proper generator is the better choice. If you need something off grid or in an apartment (running on the balcony for ventilation), a single smaller generator or 2 in parallel will work. Smaller generators also save on fuel.
At the end of the day, multiple fuel sources will probably work. Wood/coal/propane/kerosene for heat, solar/diesel/propane/gas for electricity, etc. Most grid down scenarios last less than a few days.
Being able to boil water is important as well. There are often boil alerts when there are brown outs.
$600 for one that will run your gas furnace. $15000 for one that will run your whole house. You probably want to spend more than the cheap end just so it is reliable. Or you can hook an inverter up to your car.