Only for short periods of time. If you live in an area subject to natural disasters, you'd still want a generator (either diesel, propane, or natural gas) to get you enough power during extended outages to run a refrigerator, a TV, a few lights, and charge a phone or laptop. I was without power during Hurricane Hugo for almost 10 days. Cold showers suck, but what sucked more was not getting any news.
It is the furnace blower fan that is the essential thing to power. (assuming a natural gas/propane furnace) With that you can heat your house. If you can heat your house you can have running water. Without heat you will need to shut off the water and drain the pipes so they do not burst. At that point you have no heat and no water and you probably need to just leave.
Located in the Caribbean during Hurricane Hugo?
Rural South Carolina. The apartment complex where I lived was apparently at the end of the transmission line, so we were one of the last in the area to get power back. My sister lived in Charleston at the time (where Hugo made landfall) and her VCR wasn't even blinking "12:00" when she returned after evacuating. Go figure.