Fairy and flasher wrasses are not really substrate pickers by nature and eat primarily from the water column. That is not to say they won't grab something that scurries by if given the chance, but they won't be actively competing with a mandarin for food.
My Solar Wrasse is constantly hunting for pods. He eats them off glass, rock and anywhere else he can find them. He has a feast when the lights first come on. I REALLY want a Madarin someday, but I worry about competing for food. I'm not sure if this is the case with all Wrasses, but definitely with mine.
ive never seen any of my fairy or flasher wrasse's picking and ive had over 2o different species, they might grab a piece of food off a coral or rock when i feed but havent seen them hunt like my yellow coris or melanarus wrasse