Certainly, with proper filtration/purification. You could even use “surface water” (ie, ponds & streams) if you prefilter it through a cloth then run it through a gravity filtration system.
Don’t waste filtered water flushing the toilet, though.
I’ve done some research on pool water for drinking. Turns out the main problem is a stabilizer used with the chlorine, not the chlorine itself. If you don’t use chemicals with the stabilizer, you run into the problem of water growing who-knows-what in terms of pathogens. Buy a WAPI for about $8, make sure you always have a way for heating up your water, and you’ll be able to pasteurize it for drinking. WAPIs are available at sunoven.com.