Absorbing the damage from Death Coil does not prevent the horrify effect.
Tips and tactics
Typically, Death Coil is followed up with the [Fear] spell against melee attackers, especially in PvP as the short horrify effect will prevent you from suffering casting pushback or losing your Fear spell to an interrupting skill such as [Kick] or [Pummel].
It can be used to interrupt enemies' spellcasting.
While in a five-man-instance this spell can be particularly useful when used against mobs aggroing healers or players that recently crowd controlled the target, buying the CCers or the tank time to take them out of combat or pick them up respectively. Despite for the fear only lasts three seconds, depending on the given situation you have to consider the odds for a misfortunate fear, which could easily lead to adds and as a result to a wipe.
Because of the high health return of this spell it can be used in conjunction with life tap for mana/health management.
Death Coil was premiered in Warcraft II, where it was used by the Horde unit called the death knight. It was used in much the same way as it is now, except against either friend or foe. The spell reappeared in Warcraft III as one of the powers of those death knights who serve the Lich King. This version of the spell dealt damage to living enemies, while healing their undead allies.