No. Sea urchins are primarily herbivores/grazers. Their diet:
They use Aristotle's lantern (5-toothed jaw) to scrape surfaces. While grazing on dead coral skeletons to eat algae, they do not consume the coral calcium carbonate itself. This grazing can bioerode reef framework but is distinct from predation on live coral (done by parrotfish, crown-of-thorns starfish, some snails).