Should I be able to play the unit without a battery installed?

The battery does not seem to charge in the Gameboy Advance SP (no LEDs illuminate while plugged into the charger and the battery holds a constant, low charge). When I turn the unit on, the LCD will very briefly illuminate (fraction of a second) without anything readable and then instantly go off and the top LED on the side briefly illuminates red. The voltmeter reading for the battery is 3 volts. I would assume that would be enough to power the unit, but I'm unsure. Before I expend funds on another battery, I wanted to be sure it's not the unit at fault. Shouldn't I be able to play/operate the unit on charger only (with the battery removed)? If so, then I guess I have a bad unit. Thanks for any help!