Since the results of battle are not related to one's dynamic statistics, there's no reason to make the game player-vs-player (distinct from MMO). At present, players can "battle" each other if they are playing simultaneously, but not in real-time or with any deciding factors. If there were a way to alter the odds of winning or losing a battle in-game, then your suggestion would make more sense. Overlords simply doesn't have the elements of an MMO; it's basically a text game.
It's just a game where your name and stats are recorded. It's not an mmo because you're not battling people if they're offline. That's why it's not a mmo, it tells if you defeat someone (even if they're offline.)
Lock please.