Howdy Jason, the quickest way to kill off and prevent further growth is to block the light from reaching anything that gets wet. I now, cover the clay pebbles in the net pot (six hole DWC Bubbleponics) with a piece of light weight aluminum foil with a small hole for the seedling to grow. Keeping the water temperature between 65° and 70° F will also slow or stop growth of the algae. There are additives like hydrogen peroxide, Hydroguard, Flora shield, and others that can be used to prevent or clear up algae problems.
As far as any harmful effects to the plants, consuming some of the nutrients, clogging up lines and pumps, and generally being a slimy smelly mess to add to the clean up between grows, I don't know of any. (lol) No, all kidding aside, the brown algae that grows inside around the roots, does harm the plant causing many symptoms similar to nutrient deficiencies and can stunt or kill the plant.