Well, in a tank that small filters aren't really necessary and the filters in small tank kits are usually pretty strong. If you want to you can, but you would probably need to baffle it. For small tanks I recommend sponge filters as there is really no intake that a betta can get caught in. Cycling is possible, I successfully cycled my 3.5 with no problems and it's a great benefit for me and the fish.
But in general, I don't recommend the filter that your tank came with. If you want a filter, might as well get a sponge filter.