If the amount of bleach is small enough I suppose it would be true, but I don't do that myself.
if the water in water-saucers or similar containers looks bad I just pour it out in the garden and replace it. Since I do fertilize such plants, I usually change the water every month or two due to salt build-up concerns rather that excessive algae. In larger pond or water garden situations I control excessive algae growth with floating plants that shade the water. I do want some algae in the water as part of healthy ecosystem.