The cheato isn't filter media. It's a macroalgae.
What you're describing is a refugium. Lots of people have a refugium as part of a sump, but you can have it separately too.
Like Justin said, the chaeto removes nitrates and phosphates. The chaeto, rock rubble and sand provide a place for pods to grow safely, with no predators. They eventually overflow into the main tank, providing your critters with a constant source of live food.
As Justin said also, using a refugium helps to stablize pH.