I run a severly undersized filter on my aquarium, I have a 22gal tank with a 10gal filter, but I have an exorbitant amount of plants to make up for it. I could probably do without a filter and still be good. I run a somewhat higher powered light, not a single standard T-8 bulb, but 2 T-5s instead to keep the plant growth up and I have a lot of floating plants such as Salvinia and Frogbit to keep the light levels lower where the axolotls are. I have tons of Java moss and Java fern, the moss is tied to a branch that hangs over the sand in main part of the tank.
My nitrates are always low(usually under 20ppm), nitrite and ammonia always 0. I dont do water changes as often as I should but usually do at least a 25% water change monthly to replenish any lost trace minerals and I occasionally add fertilizers.
Its definitely do-able.