Plants don't take that long to start sucking nitrates. If anything an algae farm would take longer to get established. Honestly though without any lights I don't know how effective plants will be. In a planted aquarium I've witnessed a ton of nitrate removal, but those were in ideal conditions and they were growing quickly. without any light even low light plants will not grow much. I have an axolotl tank with less than 1 wpg with water wisteria and cabomba, and the plants are barely growing. They stay alive, and still use a decent amount of nitrate(one salamander, ton of plants), but not nearly as well as they would if they had a decent amount of light, and co2/ferts. Just to recommend a few plants if your gonna give it a go, water wisteria and cabomba are my favorite two filter plants, anacharis, hornwort, are some other good ones. Basically just find plants that grow like crazy, and they should do well.