Well in a standard tank bigger then 2.5 gallons then yes. a sponge filter is easy and can come in many shapes and sizes. even custom like one of my own.
I personally have two sponge filters in my 10 gallon. One home made and one I bought. they both work wonderfully better then the other filter types in my opinion.
But seeing as u said 1/3 gallon. One third... I honestly see no amount of space for the sponge filter and plants and room for the fish as well. nor do I see it as nearly big enough just for the fish. My ten gallon houses one fish. One. But im lame by that :p
But now that I look at the post I see you might have meant 3.3 gallon tank. Makes more sense.
From what ive found ammonia can be used by plants but they also use nitrates and nitrites. I honestly cant tell you which one plants use more off.
Filters are always good though. they can prevent spikes and change ammonia ->nitrites->nitrates. Nitrates can be in higher concentrations before becoming deadly to the inhabitants in the water and are used by plants. There for a win win situation. id say go with it. Make your own spongey.
This guide made the most sense to me and explained everything and allows you to make your own size. Tiny!
I also suggest to use products from amazon to lower the costs. Thinks like an Whisper airpump and tubing is much much cheaper. Ask questions for anything and ill answer. this was hard for me the first tim but I learned along the way :P