I mean, the way the various cards save is kind of like save states right? So you can't really have real-time Nintendogs right?
No, the game saves just as it would with a normal DS game, Nintendogs will run just as normal, though GBA games can use savestates if you want, DS games can't.
if you do not save the game say if you had a gold bar and you turend the nintendo ds on it will not de there