Yes, copper at high enough levels will kill algae. The problem is, the required concentration of copper needed to act as an algaecide is very close to the concentration of copper that is unstable in pool water. Therefore any high chlorine or pH levels will likely cause copper scaling. On plaster that leads to staining that is very hard and expensive to remove. Once you build up too much copper in your water, you have to drain your pool, there is no other way to remove it. Copper does nothing to kill bacteria or viruses or oxidize bather waste. So you have to maintain a low chlorine residual in your pool water. It is very difficult to maintain low levels of FC consistently and homogeneously in a residential pool (circulation dead spots). Therefore you will likely not have proper sanitation levels most of the time.
Leave the copper ions for keeping decorative water fountains clean and use as a root killer...don't put copper in your pool.