I don't think that they eat healthy coral.; there isn't anything I've found or observed to suggest they do. If someone has a link to information to the contrary ;it would be helpful. They do,however irritate croal ;the spines may pierce coral flesh creating an infection site and they are notorious bulldozers;oviously , corals don't do well when knocked about. I've have seen them perched on coral, perhaps feeding on zooxanthellae and other excesses the coral expels from time to time. I've seen corals suffer from this activity.
They do eat coraline algae ;coraline is generally beneficial to corals and reef building since it is calcareous and forms calcium carbonate for skeletal mass; like corals do. Coraline cover also wards off some nuisance algae as it competes for nutrients and provides a surface less suited to invasion by hair algae, etc.