Copper keeps algae and moss at bay because it is a very effective herbicide. I would guess that keeping copper in a s/h pot would likely have detrimental effects on the plant as well as the algae.
You basically have three choices - block the light from entering the pot, periodically treat with Physan or bleach, or don't worry about it.
I do a so-so job with the second option, and put the pots in decorative containers when I bring them in the house.