Yes, it's (cyanoacrylate) quite safe when used properly and rather effective for many corals. Generally, less glue is more effective. Too much in the wrong places, as stated above, can burn the tissue and/or cause it to die.
It can definitely be completely useless for some corals -- leathers and Xenia are ones that I don't even try to glue. Basically, if it slimes when handled or cut, it's going to be very difficult to glue.