No, the Life Orb will only activate (and thus drop 10% HP) if you hit a non-Status move and it successfully deals damage. Dark Void and Will-o-Wisp are status moves, unaffected by the Life Orb.
Pokemon with the Sheer Force ability are capable of using attacking moves and getting the Life Orb boost, but never taking damage from it, so long as they use a move boosted by their ability.