You cannot safely swim in a stagnant untreated pool! There are several reasons. First, though it is rare, pathogenic microbes can grow in a pool on their own. If you want to scare yourselves, read about Necrotizing fasciitis - Wikipedia or “flesh eating bacteria”. read more
If the bottom of the pool feels slimy, dump the water and clean the pool. And use the pool water for other things: water potted plants, the garden, the lawn. Keep the water for a few days is fine as long as you can keep it clean. read more