Sure, the frogs will cycle the tank. The tank will be cycled to handle the bioload of the frogs, so when you add the betta, be sure to watch ammonia and nitrites (or just do frequent changes for a couple weeks) to make sure they don't get too high. One betta really shouldn't cause too much of a disturbance, but it's best to be safe. Would be a shame for his fins to just get messed up again once you get him all healed up 
