For a short time maybe but not very long if you have fish and even if you don't. Although a way to get around a lot of it would be to use a powerhead for circulation. Without circulation there would be serious issues with dead spots, anaerobic pockets as well as aerobic pockets. sulfurous gas possibility and just a lot of other things that could go wrong and do it in a hurry.
Anything you do without a filter you will need a huge mass of plants, a very light bioload and a little if not a lot of luck. To even consider it I would not try it with anything smaller than a 55 gallon tank just to support the plant load needed to keep the tank as balanced as possible.
This is what I know of it without trying it and from others that have tried and seen even just a planted tank fall apart without at least good circulation. If there is someone who has success with it, short of putting one plant and a betta in a 10 gallon tank I for one would like to know what they did and how well it worked out.