Yes. The main purpose of the filter is not to remove solid waste but rather to serve as a place where beneficial bacteria can live and grow. These bacteria process the toxic ammonia that your fish give off into nitrite and then into nitrate, a substance that's much less toxic to your fish. Without these bacteria, ammonia levels in an aquarium quickly climb, leading to dead fish. Check out the links I posted in your other thread about the aquarium cycle to learn more about these bacteria and the aquarium cycle in general.
The sponge filter Pasfur mentioned is very good at providing a place for lots of these bacteria to grow but it isn't powerful enough to suck up small fish fry, which makes it ideal for fry tanks.