yes you can, but i don't see why you would want to. If the MagSafe cable comes out, your computer shuts down instantly. It also downclocks your CPU to 1GHz, for what reason i don't know.
It's usually best to leave the battery in to prevent dust and grime building up near the connectors and causing damage to your machine. If calibrated properly and regularly (monthly), the battery won't overcharge and leaving it plugged in will cause no damage. Having said that, I don't think the iBooks will run at all if the battery isn't plugged in.