It could, but you would need a good bit (more then fist sized) and have rather strong light on it. Chaeto will survive under low light but it will grow very slowly. Dosing iron can increase its growth rate.
Many people don't like the look of chaeto in the DT, but it is a great refuge for various pods. I keep a fist sized ball in my DT in the back out of view, but it often comes loose from a crab foraging through it; very annoying to have a ball bounding through the tank.
Dosing carbon can help with both phosphates and nitrates by fueling bacterial growth. Vodka, vinegar or sugar are common methods.