How can I access the water in my pipes during a supply outage?
You are correct that you should be able to get a dribble of water out of your pipes this way. But you are probably overestimating the usefulness; my guess is you have less than a gallon in your entire household plumbing. (Of course it depends on your home and you can do your own estimation based on pipe size and total length.) One toilet flush uses about 1.5 gallons (or more, depending on the design).

If you want to have access to water in an emergency I would suggest storing some yourself. You can buy large water jugs at most supermarkets. You can refill a toilet tank yourself by just pouring water into the tank until the float lifts up. And/or if you are expecting a service outage you can fill a bathtub with water.