Sure, most mobile platforms that have a lot of development on them have emulators of some sort. Not a perfect match as you'll be off on actual CPU speed, but you can usually limit RAM on emulators to a realistic value. There's a nice ARM emulator for Windows Mobile, for instance.
No idea about this particular platform, though, but if it's a major one, I'd imagine that there's probably an emulator somewhere.
You will probably not want to run a battle.net connection from your phone, however. That is going to wake up your data link frequently, at least for SID_PING/SID_NULL, and that's going to completely hose your battery life. I'd be surprised if you got even a day between charges like that. Battery life for a device like a cell phone is dependent on keeping as much of the device powered off for as long as possible, and frequently waking up to perform network tasks does not mesh well with that philosophy.