No plants dont need filtration, in fact, they are the filters! I actually use them as filter in my lone betta tank. I dont even use lighting, or co2 injection, the reason being I use Anacharis. It uses indirect bright light, and because I have hardwater, gets all the carbon it needs from the water itself(anacharis is one of the few plants in the trade that can do this).
There is actually a part of the hobby called natural aquariums, this involves using low tech stuff, and using soil as a substrate. No filters and possibly, no heater(if you live in the tropics) and just using plants and the science behind how they grow(most plants prfer to root in mud dont they?). You can check out
natural aquariums.com
really great site