But do you need the chlorine any more after it's killed off all of the bugs in the water?
The first time you break a seal on the water, put a pump or siphon hose in it, or just don't get it
quite sealed back up after it's been treated, you can/have admitted "germs". My wife, the nurse, tells me that any "sterile" water container that gets opened is pitched out after use, regardless of how much remains. You can culture some really nasty stuff in untreated water. Pseudomonas comes to mind...
Now, all that being said, ya gotta have water, and any water is better than no water at all. Don't let Perfect be the enemy of Good Enough. BTW, chlorine bleach in bottles loses chlorine over time, just like treated water. If you really want to store chlorine for use at some future date, get a pack of dry swimming pool treatment sodium hypchlorite. It's cheap, a zillion times more concentrated than Chlorox, and has a near infinite shelf life. It's ususally sold as a shock treatment for the pool. Get that with no other active ingredient, like fungicide or algicide.