I would be surprised if a program like this couldn't run for over 10 hours on an iPad without neededing a recharge. The worries about battery life confuse me. Even in extreme cases there are external battery chargers on the market pretty cheap. If you are in a tourney using this app only it would be a smart investment i guess.
On the stat tracking for development: I think if they were doing this, which I doubt, they wouldn't tell us. There are all kinds of people out there that would skew data. I think tourney results are a better indicator of competive trends than daily app data.