A self sustaining system would be very possible, but not in the scale that you're picturing. The primary source for any ecosystem is the sun. You must have a system that makes good use of the sun. This must includes both multicellular autotrophs (plants) and unicellular autotrophs. Then you have the things that eat them ("herbivores", but not quite an appropriate term for things that eat algae). This appears to be where your misconception comes from, as this is usually daphnia, midge, and other such little critters, and not fish. To may knowledge (and this very may well be wrong), there are no fish common in the aquarium trade that can survive on algae/plants alone, as even traditional algae eaters like plecos and otos spend a decent amount of their time rooting around for these in their natural habitats (as I said, correct me if I'm wrong). Next comes your omnivores and carnivores, then secondary predators, and then tertiary predators, etc. Many of these dietary needs are non-negotiable. Just like how humans couldn't live at sea for long periods of time living on salted meats and thereby forsaking their need for essential vitamins from plants, fish can't live on duckweed alone. Scurvy was a great killer of men for many years before solutions were found.
A common concept in ecology is that there is a roughly 10% transfer of energy between rungs in the food chain. That means that if you consider the entirety of energy coming into your system from the sun, 1% will make it to your fish. That's simply not very much at all.
Another thing that you haven't addressed (or that I missed) is conservation of matter. Most fish don't eat plants. How do you replace the nitrogen that gets locked up in plants? What about other minerals and nutrients, like phosphates? You will eventually have to compensate for this.
Here's how I would approach a problem like this: First, find a 10g thats longer than normal ones to increase it's side area. Next, fill it full of heavily fertilized water (like 60-100 ppm nitrate, etc) and stick it in a south facing window. Wait for the green water to come (and hope that it does, algae serves no master). When you're nice and greened, get your hands on a daphnia culture and seed the water with it. The daphnia will eat the GW and begin to multiply. Let the population come up, and then introduce a SINGLE fish, like a white cloud or something. He'll have a ton of food for a while, and hopefully the tank will balance itself out between the GW, daphnia, and fish. Maybe you can add more, maybe not, you can't predict that. Notice that no plants were added into this system. As nothing eats the plants, they are a dead end to the food chain, and we're trying to shunt all the energy we can to the fish. Also, omnivorous fish like platies might be okay here rather than a few WCMM, as they will be able to eat other algae sources to supplement the daphnia predation.
