If you are running a canister filter or reactor I would guess 2 weeks to a month. Depends how dirty the water is. The carbon is exhausted when it has absorbed a certain amount of waste. I have heard that it continues to remove trace elements after it is exhausted but I don't have a way to confirm that. I believe you will remove the toxic material that corals produced when they fight another coral. That's my opinion.
It will also clear the water so light should penetrate further and brighter. the change in light penetration could stress some corals.