As long as your level is low, I don't think you'd have a problem. Some city water comes out at over 1.5ppm of chlorine and that doesn't seem to affect stuff. I remember testing the water at my first house one time, the chlorine level was literally 1.5ppm. My grass was very green and my flowerbed looked great.
I used to shoot chlorine gas into pools in a former life. I burned some plants with the gas sometimes, but even that didn't actually kill them. And that was with 100% gas chlorine.
Now, I can tell you, if you breathe too much, it may affect the way things smell and taste. I know that from firsthand experience shooting the gas.