The P1D was not designed for a LiIon rechargable, so the circuit will be bypassed and the LED will run direct drive from the battery.
Med and Max will appear close to the same brightness and you will lose low altogether. Med is actuallly a bit lower and longer running but you can't see much difference.
In some very rare cases the circuit or LED can be permanently damaged, but if you only run it for a few minutes or have active cooling that should not be a problem.
If you run LiIon your warrenty is null and void.
If you run a search on the reviews forum I know there are runtime graphs for that light and LiIon battery.