Cold-water corals have a few surprises though. In the late 1990s while debate raged over the potential damage deep-water drilling could inflict on cold-water corals, they were discovered growing on oil platforms in the North Sea - even on the Brent Spar, a cause célèbre in its own right (you can read more about the Brent Spar case from Shell and Greenpeace along with a summary on Wikipedia).
Further work has shown that many Lophelia colonies have been growing close to sites where drill cuttings have been released over the years. ROV surveys have shown that in some places half a colony has been smothered by drill cuttings - but the other half is apparently healthy.
Much more work is needed to understand how reef framework-forming corals like Lophelia pertusa deal with sediment exposure before we can judge how sensitive they may be. After all, cold-water coral frameworks trap sediments, and many corals have been photographed growing on rippled sandy seabeds where the corals are likely to tolerate sediment exposure.