If I had meant that chloride would evap off, I would have written Cl-, the notation for chloride ION, where Cl is simply the notation for elemental chlorine.
Luckily, I am aware that the negatively-charged chloride ions would have to combine into Cl2, Chlorine GAS, before evaporating off. The presence or absence of other chemicals (including dissolved O2), and pH levels, in the water drives this equilibrium.
Bleach in the water isn't good for plants- most plants are pretty sensitive to sodium. They need a small amount, but too much is deadly.