PvP PvE? PvE PvP?

Is it possible through careful manipulation of player experiences and interactions to make a PvP experience feel like a PvE experience for one side, without making the other side feel like they are constantly being defeated? If a player monster is able to interact with multiple instances simultaneously, it might work. They could have separate "health" scores for each instance, and "dying" in one just causes them to no longer interact with that instance, instead having it get replaced by another. From the monster's perspective it could seem that they never actually die, instead the heroes just keep disappearing. If there is a score system for causing havoc and harm to the heroes, the monsters could compete with one another for points, and brag whenever they actually get a kill.