It really just depends on tap water in question and the plant species. I've kept Lobelia Cardinalis and mosses in glass bowls in a window sill for months sitting in tap water. No ferts whatsoever. They did just fine. I even kept carpeting plants like HC, DHG and monte carlo in the same spot for a few weeks in tap while I decided what to do with them. They did okay. However, I have melted crypts and other softer stem plants by doing this. These plants don't fair well with change but they will usually adapt if rhizome stays alive. My window also faces east. If it got anymore than just a little morning sun, things would be very different. The nutritional demand would exceed the conditions of my water and temperatures would be quite higher. I feel like my plants are in energy saving mode and when they finally get planted in ideal water conditions, their growth takes off very quickly.
As for the chlorine in my tap, I'm not sure what the levels are but it doesn't really seem to effect my aquatic plants. When watering our outdoor garden or making compost "tea" we just add a little molasses to react with the chlorine. The effect is instantaneous and microbial activity doesn't suffer. Anything organic will react with chlorine and neutralize it. It doesn't take much.