If you run it through most camping filters it will be drinkable if the salt and heavy metal content is not too high, but the chlorine and organic compounds will tend to wear out or use up the carbon much faster than normal.
If you run it through a big carbon block filter and then reverse osmosis it it will be fine. The carbon is required before the RO membrane because just a smidgeon of chlorine will eat the membrane. The membrane should filter out most anything remaining.
If you distill it and run the distillate through a carbon filter it will be fine. Distilling can carry many volatile organic compounds with the water. Carbon filtering can remove these if the filter is efficient enough. This can be partially avoided if the water is brought to a heavy boil driving off most volatiles at the start and that first steam allowed to escape before starting to capture the rest of the steam.
By the time the chemicals are out of the pool water due to breaking down and evaporating, or combining with stuff in the pool water, the other stuff in the water will start growing all kinds of nasty stuff, so a "safe window" may be awfully short if all you are concerned with is the added chemicals.
Adding chlorine to the pool will kill most "germs", but it does not remove anything from the water. Chemical treating of any water does not "purify" it. The bodies of all killed microorganisms, the skin cells of swimmers (and worse secretions), the bugs and spiders and leaves etc. are not removed from the water by the chemicals. Some of the chemicals make the pool filter able to grab a bit more of all the junk, but not much. Worse, the action of chlorination on organic compounds inherently adds carcinogenic and other organic compounds to the water.
Boiling the water will kill the living nasties, and drive off much of the volatile (low boiling point or low vapor pressure) contaminants. On the other hand, any remaining chemicals, salts or heavy metals (lead, cadmium, arsenic, uranium, plutonium, etc.) will be more concentrated than before boiling off some of the water. This can definitely kick marginal water into EPA failure. Short term this is not likely to be a big deal, but long term it can accumulate terribly.
Running the water through a Dalton or Berkey type ceramic filter will remove almost all the living nasties, and most of the bodies and twigs. It will not remove salts, heavy metals or organic compounds. Adding specific filter media for specific contaminants will help but starts to get really exspensive if you want to filter out each possible metal, compound and salt.
Drinking unfiltered pool water for a week or 2 will almost always be better than dehydration and death. However there is a distinct possibility that you will wish that you had died before you get better.
