A heater is also generally a minimum for betta's unless you live somewhere really warm, they need to kept at 76F minimum and they prefer closer to 80F.
Without cycling you will need to be prepared to do regular water changes a few times a week, there is a recommendation thread for water changes in the bowls and habitats section.
If you were to use prime water conditioner that also detoxifies ammonia and nitrite to a less dangerous form, and you can use that up to 5 times the amount.
If you are prepared to do the above a Betta should be fine in that size tank. You could also add a small filter and cycle it. That size tank would cycle.
Last edited by beautiful Betta; 04-29-2014 at 08:01 AM.