it is pretty hard to raise tadpoles, so while they may breed and lay eggs, they probably won't hatch or survive. your betta or frogs will eat them, or they'll just die. you could also get all females or all males, then there won't be a problem. if you do get three frogs, it's recommended you have more females than males, so a 1:2 ratio of males v females.
They will likely breed regularly, but the eggs will not survive without your intervention in an aquarium setting. They are extremely difficult to raise, it is rarely managed by hobbyists at all. So you simply are not going to have to worry about them reproducing successfully just by keeping them in the aquarium. The Betta and the frogs will eat the eggs as soon as they find them - from my critter's behaviors it seems the eggs taste quite good. You will likely see mating behavior fairly regularly, though - the singing of the males, the sometimes hours long hugging/mating process known as amplexus, and then all the animals in the tank eagerly eating the resulting eggs.
While Bettas and African Dwarf Frogs usually work, keep an eye on your Betta's fins. Frogs are nearly blind, and sometimes will latch on to long fins that they see moving because they can't tell from afar if things are edible or not. Worst case, your Betta's fins may be badly torn by this behavior. Of course, watch to make sure the Betta does not pick at the frogs, too. It might be good to have a backup tank ready just in case.