This probably isn't a good idea. the pi-top's battery right now is flaky at best. if you can get it to work, without the pi, if you drain the battery completely, it may charge, but in my experience , won't run until you apply the firmware patch again.
for example, I drained my battery with the pi in the pi-top and then charged the battery back to full and unplugged the power. I tried to restart the pi-top and had no power from the battery even though it is fully charged. I had to plug the wall adapter back in and run the firmware patch on the pi. after that patch succeeded, I was able to unplug the pi-top frm the wall and run it from the fully charged battery.
but, go ahead and try without hte pi and see if ou get a different result.
the answer is there.
I don't know if it has been mentioned before, regarding the firmware patch, and WHY it works, so here it is.
If your battery voltage drops down near zero volts, the charging circuit will not attempt to charge the battery. This is probably a safety measure to prevent battery fires if the battery were say shorted. The problem in the charging circuit is that it does not disconnect the battery if capacity falls below a certain level, say 30%. This is a good established limit for LiPo batteries. Not sure what's in the PT.
If your voltage is near zero, and you apply the firmware patch, what actually happens is that the charging circuit loses is mind for a moment, and allows current to flow into the battery for a few seconds. At first, this won't be enough to get the circuit going, but when you apply the patch several times, the cumulative effect is that the battery gets enough of a charge that the circuit no longer thinks it is unsafe to charge.
The patch itself does not change anything in the on-board firmware after the first install, it just that applying the patch always results in some registers (might be the wrong term, but hey) being reset, which results in the momentary charge being allowed.