A lot of kava bars definitely re-use any kava that wasn't sold/consumed by refrigerating it over night and then serving it the next day, so it isn't rare. That being said, I would definitely recommend that if you are going to drink kava that you prepared the night before, it should have been refrigerated overnight.
As far as kava getting more potent by just sitting there, I would be a little curious "how" that would actually work since the grog can't absorb any kavalactones since they are not water soluble and our kava (as we know it) is a suspension and not a solution.