Dog has died on me. Twice. He doesn't eat Ghost people for me.
The ghosts have to be unconscious and not dead for Dog to do his devouring thing.
It helps if you target the torso and not the limbs and it also helps if you don't have the "ghost hunter" perk which kills ghost outright instead of KO'ing them, though if you do have the perk, you don't really need Dog for ghost killing anymore, you can go with the God personality and take advantage of the sneak and trap bonuses.