Potentially, but only once the plants are well established. I run mostly eco system tanks, including filter less, where the beneficial bacteria in the deep substrate and plants do all the work. But the plants need a few weeks to become properly established (root system), usually with some help from fertilizer tabs. Until that happens, where there has been plant die off and with a fish in cycle, you will see cycling particularly in that size tank.
If a rimless tank, you can also try growing houseplants with the roots in the aquarium (e.g. Peace lily, pothos... Wash all the compost off first) as they are significantly better then submerged plants at removing amonia, nitrite and nitrate from the aquarium.