No, it's a really bad idea for a number of reasons.1. Male and females should not be housed together as at least one of them will end up dead sooner or later. Bettas should be kept as either single males or a female group.2. Bettas are tropical fish which actually prefer higher temperatures than many tropicals and as such are not suitable for an unheated tank.3. There are no fish which can live without a filter really. Even if you change the water every day, ammonia will still build up as fish create it not only from their waste, but also just breathing. The best you can expect in this situation is a greatly shortened life, but they will likely die from illness before that. There is such a thing as a walstad tank, where you have enough fast growing plants to process the ammonia, but in all honestly they're high tech and they're a hell of a lot of work.You're right that they won't go in your 350L tank either, as the guppies would probably shred the tails of a betta.A male betta on its own in a small tank with heater and filter would be fine, and you might be able to house a group of female bettas in your 350L if you have stocking space left, but I would advise you to do your research.Depending on what your room temperature is like, there are also some temperate and coldwater fish which may be suitable for an unheated tank, but there aren't any fish you can keep in an unfiltered tank.