There are already MMOs on mobile devices and there are already some games on these devicess that outperform the graphics quality that is on some of the games released on the current generation of consoles or PCs.
The only problem is that these games do not sell very well because people do not have the time to sit playing them on a mobile device. Mobile gamers prefer short 2 minute bursts of gaming.
The successfull mobile MMOs i've seen are pretty much only using indirect interaction between players (Which makes it doubtful if they really can be considered MMOs), the OP however was talking about using a mobile/tablet app as an addon to a desktop MMO,
WoW allready does this (allowing players to buy things from the auctionhouse, chat with their friends/guildmates, etc using their phones) and could probably do their pet battle thingy on mobiles aswell (it sounds as if it works in a way that could play out fairly well with high latency 3G connections and short 1-2 minute play sessions)