This is a discussion on Can I turn off my filter? within the Aquarium Plants forums, part of the Freshwater Fish and Aquariums category; -->
I have a 29 G tank and it's Medium planted. I recently put in the fish stock which is:
9 neon tetras
that depends entirely on the nutrient uptake in the tank and the nutrient input, so this is not an easy question to answer. Even if your tank is fine running filterless, you still need some form of water movement. I could list a number of reasons why you need water movement, but one of the things water movement does that nothing else can is evenly heat the tank. I beleive it is possible to run a stagnant tank, but I doubt your tank is in a warm enough environment and it is quite risky with the stock you have. Running without a filter is certainly possible with planted tanks, but you must be very careful when doing this. I run one filterless tank and another tank is only filtered when I am awake.
It all depends on how you define medium planted too, it would be helpful to see a picture and know what kind of plants you have in your tank. All of my tanks run at close to 0 nitrates due to the high level of plants and low level of stocking, I even go two weeks between water changes because I have become lazy, but I still run sponge filters for the simple fact of at least they move the water around a little, but its not uncommon for the top of the water to be 4 degrees warmer then the bottom of my tanks, the fish don't seem to mind much. As for biological/plant filtration you should be fine if it is planted well enough.
IMO plants don't need current. I run a completely stagnant 1 gallon and it is often my clearest happiest lil' puddle ever. Cherry shrimp in there are always happy too.
I would not be surprised if your tank can run filterless. My 15 gallon is pretty heavily planted and has just as many fish in it. It uses just a powerhead to circulate water. I have been thinking of replacing it with a lower powered one too as it seems to be making too much current IMO.