Many people grow chaeto and other macroaglaes to reduce nitrate. The chaeto uses the excess nutrients (from waste and uneaten food) to grow, reducing the amount of nitrate in the water (which helps limit nuisance algae growth in your display tank).
Chaeto would not replace your need for a wet/dry filter. If you have bioballs, the bacteria growing on it is what breaks down ammonia in your system (same bacteria as on live rock). Chaeto will not break down ammonia, so it can't replace the wet/dry. If you have trouble with algae in the tank or high nitrates, growing chaeto in a refugium will help. But you can't replace the wet/dry with just chaeto- you would need other filtration (could just be more LR).