Sorry to bump, but just wondering if I could get a definitive answer on how much damage this does to the battery. I can only seem to find FUD or confusion on this subject.
The battery manufacturers say not to.
So you shouldn't, in my view.
But you can get around it by the wonder of semiconductors.
You can wire up the device so that when a + voltage from the charger is present, the battery --> game connection is cut off and the voltage from the charger is the only thing that is presented to the drain represented by the game boards and screen.
I'd have to think about it more, but I think you'd use a P type FET to shut "off" the connection from the batteries to the game when a high signal is introduced at the gate from the + pole of the charger through a diode, and then two legs from the charger (one to battery + and one to your game regulator/boards) each isolated from each other via FET based synchronous rectifier configurations (to get over the problem with forward voltage drop that would result from just using pure diodes). This is what takes place on some level in a laptop when you plug it in.
The problem, as I see it, is that most LIPOLY set ups I have seen charge the cells on a per cell basis, so the charging voltage will only be 4.25 volts anyway. and wired to the cells in your array parallel to each of them.
For all the work involved, I don't think its worth it. I'd think a switch with a "charge only" mode would be best.
If you set up a good battery set up, you should be getting a couple/few hours of battery playing time, and then just let it rest while it charges.
If you must play with it plugged in, simply add a second jack with an old fashioned AC adaptor. And a switch that completely separates both ground and + of the batteries from the rest of the system when charging.