Would you be able to function with just the ignition/control and no fan in an emergency situation? I'd MUCH rather temporarily be forced air instead of blown than to have to deal with gas/generator/dude swapping it with a mower.
Nope. Without the fan running, the control boards will not let the unit continue to operate. Plus the fact that a forced air furnace with no fan has no means to get the heat thorough the ducts and to the people.
A small generator (1500 watt) will start and run an average forced air gas furnace. It won't do much else, but at least you could have some heat. Furnaces are typically on their own circuit, so a generator and a transfer switch can be used to power just that circuit. There are other creative ways to get power to a furnace circuit as well, but they don't meet code so I won't be discussing them here.
Fresh water was brought up. It is a huge concern over the long haul or in a situation like Katrina. In our case last January, with some searching, we could find bottled water after the first 48 hours. We could also go into the city and get water from the municipal system. When we knew that the storm was coming, we filled all our bathtubs with water and several large plastic totes with water. If you're on a well and the power goes out, you soon lose the ability to flush your toilets. Having a 3 gallon bucket and some water in reserve, will allow a toilet flush for the inevitable chong.

You can also boil bathtub water to drink in a pinch, assuming you have a means to boil it.
At the end of our 11 day stint, we were getting pretty good (almost comfortable) at surviving without power and running water. Even though the experience sucked *alot* I did learn much from it.