no such thing as overcharging with lithion-ion batteries. these type of batteries have built in protective circuits that shut off power when the battery is full. what kills lithium-ion batteries is fully discharging it!
The only reason one should run the laptop using battery power only is when there is no power outlet nearby available or you just want the convenience of using the laptop without the wires. I have a desktop replacement laptop and have always used the battery with the ac adapter plugged in all the time(Only used battery when I was on a plane.). Running for at least 8 hrs daily and sometimes running for 6 days continously. I'ts going to be 1 yr old next month and battery performance is still the same as it was brand new. I still can get about 1 hr heavy gaming on just battery.