Sorry, I posted at the same time as Mr Snailz!
Does what?
Cycling with a betta or any fish with a labrynth organ (can breathe at the surface to some extent) is just as dangerous as with any other fish. More so actually since these fish are insanely overbred and thus are very delicate. Ammonia can damage their gils and fins, and being able to catch a breath at the surface does not protect them from the damage from nitrite.
Better to cycle with some kind of snail, because some of them can actually leave the water when it gets d
icy and go somewhere else.