There are DEFINITELY a lot of beneficial bacteria in the gravel, enough to keep the tank going for 24 hours. Yes, they need oxygen but oxygen depletion in water does not happen overnight. This is why many people successfully keep fish tanks without filters, just with lots of bubblers. Obviously those kinds of tanks take a lot more cleaning because the filter does the majority of the cleaning. A filters 3 jobs consist of bacteria breaking down unwanted toxins (those bacteria also live within rocks and decorations within the tank), mechanical cleaning to rid of waste and matter, and thirdly, to put oxygen back into the water. Plants also act as a natural filter. So in reality, there shouldn't be any change in your water at all. Plants photosynthesize to create more oxygen from the carbon dioxide within the tank, however if there isn't enough carbon dioxide in the water, the plants will use photorespiration, where they take oxygen from the water and convert it into energy. However, they don't normally do this unless they are in desperate need.
Needless to say, in reality, you don't necessarily need a filter if your tank has plants in it and bettas, that being said, more water changes and cleanings should be done to maintain water quality.