I doubt you could keep something that small cycled, especially since you'd be changing at least 50% of the water every three days (one would hope). From my understanding it's not even worth cycling such a small container, as it would be hard to keep the bacteria population. Just do the water changes and cross your fingers. And if you wanted bacteria to lessen the amount of water changes you have to do, it's not going to help.
Of course the standard ammonia build up/heater disclaimers apply to such a small container. Length is important for tanks, but it's not the end all be all aspect of the container. Especially for bettas, I'd consider water volume *far* more important than length, since they are adept and adapted to swimming from various levels to the top of the tank, they take in oxygen, so the surface to air ratio is less important, and they can put out a decent amount of waste.