A long while back people use to keep and grow marine plants in their reef tanks. The problem was that the plants could take over the tank and grow into the coral skeletons or on rocks and you would have a hard time removing it. Also some fish would eat it all. You also have to worry about some plants going asexual in the tank. So you need to be careful which type of plant you put in the tank and keep it in check by harvesting it as it grows.
I had a tank with just an anemone and a Clown fish and I let the plants grow in the tank, mostly across the top of the tank, with the return water flowing over it, everything was fine and I didn't have any problems, outside of having to harvest the plants over time.
