Will it run without the battery?

The battery is dead. It powers down within a minute or two after I unplug it. I'm concerned that the battery could develop issues, since it's dead and under charge 100% of the time.

Can I just pull the battery from it and reassemble it? I only use it plugged in at the moment. I realize it sounds weird, but it's an old iPad. (It's in the 'old folks home' part of its life) I really don't see using it seriously as a battery powered iPad depending on the battery, so why replace it. I just want it to be 'safe' if the battery decides to swell or overrun. In other words, I can't afford to replace it, and see no need to replace the battery, but would like to keep it working. Long question, I know...

Thanks...