I have a 10g that I planted with 5 small sickly water lettuces and 2 red mangroves. It has no fish, but a lot of snails that hitch hiked on some plants. I set it up because I was curious to see how well the plants would handle nitrates etc. Each week I drain about 30-50% of the water and refill with water from my CA/SA tank when I do the water change which leaves a nitrate reading of around 10. By the end of the week the nitrates in the 10g are at zero. Also the tank is blanketed now with big healthy water lettuces and the mangroves are growing nicely.
With no fish in the tank this is not exactly impressive, but I think it has potential as one possible approach to using plants to help filter a tank. A stand alone tank, perhaps in-line with a sump or canister filter could be an interesting display all by itself. The use of immersed and floating plants works well for a number of reasons. First, there is no need to add CO2 because the plants get it from the air. Second, the floating plants (like my water lettuce) can grow so densely packed that there is minimal evaporation (I don't observe any water level change over a week, of course there is no water movement either). Third, as a display tank, the tank itself could be hidden, since the surface is what is on display with it's lush plant growth. If it was drilled you wouldn't have to even see the plumbing.