You don't need one, but you will need to change the water every other day. Betta's will constantly build bubble nests resulting in a nasty film over the water, or at least that has been my experience. I have a wally world 5-15 filter on my 5 gallon Betta tank, to slow the flow I just lift the tube a little or stick some porous sponge in the tube. Alternatively you could get a cheapo sponge/airstone type filter. Or even some bushy floating plants to slow the flow.
So, can it be done, absolutely yes. Would I recommend it, no, not in the long run.