Though it is not necessary to have a filter, there are some benefits. There is also the matter of the current which is important.
First on no filter; I had a 10g tank set up as an experiment (for me) with no filter. It had a heater. Sand substrate, planted with chain swords and a couple larger swords, and floating pennywort. Fish consisted of 10 pygmy corys, 11 Boraras brigittae, a couple shrimp (this was not planned, they came in the bag with the corys). I placed the tank in a west-facing window so I could do without a light. It worked well for as long as I had it running like this; the less-controlled window light made algae an issue, and also it is difficult to see the aquascape with a rear light source, so after about 8 months I moved it and added a light and a sponge filter. The latter kept the water much clearer, which leads into my next point.
A filter that is solely mechanical (passing the tank water through media to remove suspended particulate matter, with no chemical filtration) does benefit. This microscopic matter can settle on plant leaves, slowing or preventing the exchange of nutrients. A gentle current is also useful for this. But nothing strong, like a powerhead down the tank, as this can prevent the plant leaves from taking up some nutrients. Biological filtration is unnecessary, and in fact detrimental. Most aquatic plants prefer ammonium (ammonia), not nitrate, as their source of nitrogen. They compete with bacteria for ammonia/ammonium, so you don't want to be encouraging nitrifying bacteria, hence no biological filtration beyond what is naturally going to exist in any aquarium. Plants (aquatic) only turn to taking up nitrate if there is insufficient ammonia (and some think then nitrite) to supply their needs in balance with everything else. Plants have to convert the nitrate back into ammonium before they can use it, and this wastes energy.
One comment on nutrients. Without fish, nitrogen will be less in a plant-only tank. As mentioned above, aquatic plants prefer ammonium (ammonia) as their source of nitrogen, and this comes from fish respiration as well as the breakdown of organics, and fish obviously means more organics than without. I have a 20g that runs with just plants permanently; I use this for my new fish QT, but it can run for 8-12 months with no fish. I have noticed that plant growth is slower in this tank; when I add new fish the plant growth does show a positive response.
Hope this helps.
Byron.
