CC has the same use as with using liverocks or aragonite / calcareous sand, which is their ability to serve as 'buffers'. But given their composition, they will become phosphate sinks in the long run. Just like sand and liverocks. (phosphate just love to attach on calcium based substrate).
Sand would be better (more efficient most of the time) if your purpose is to lessen nitrates (more surface area). The only plus side to adding crushed corals would be a sort of refugium for copepods and amphipods. Crushed corals may still help with denitrification but not as efficiently as other means.
Anyway, as for matrix you can put it either in a large media bag or in a reactor. The key is low flow.