For those of us old enough to remember the batteries that had to be checked regularly, then refilled with distilled water. Those type of batteries were a good source of lead, and the only hazard was the sulfuric acid.
Modern maintenance-free batteries have the above listed added chemicals to make them never need filling. In fact, they are sealed permanently, no way to check the water/electrolyte levels.
Modern maintenance-free batteries have Calcium in the lead which makes the recovered lead from them as bad for casting as would be Zinc in the lead. If you mix such lead alloy with your bullet alloy, you will end up with a great deal of lead alloy that will not cast a usable bullet.