Yes, cory catfish need a bubbler. Even though cory catfish can swim up to the surface and gulp oxygen in order to breathe, a bubbler or air pump will provide consistent oxygen in the water. Too little oxygen in the water might eventually cause your cory catfish to become stressed or even fall ill.
A bubbler provides some agitation to the water to help replenish dissolved oxygen. With more oxygen in the water, your cory catfish can live more comfortably in the tank.
Additionally, cory catfish love playing with bubbles, so the bubbler can also act as a source of entertainment for your corys.