Is there such a thing as natural blue coral?

Answer 1

yes. Latin name is Heliopora coerulea. Living specimens are brown, blue-gray, or gray , but the skeletons of dead heliopora are blue---so it is prized for its color.
Called blue coral, blue ridge coral, blue fire coral.

Photos:
http://www.nps.gov/archive/npsa/NPSAcorl/Helcoeru.htm
http://animal-world.com/encyclo/reef/soft_cor/bluecoral.php
http://www.coralreefecosystems.com/gallery_corals.htm#Heliopora%20coerulea
http://www.arkive.org/coral/Coral/heliopora_live.html