The railings are covered in plexiglass - making it impossible to scale. (Some are solid metal) The doors are challenging for adults to open (our stateroom host had to teach me) and lock high up.
Concievably, a child could pull the stool over, manage to unlock the door get out on the veranda, use the veranda chair to launch himself over the edge. With hundreds of children on every cruise, it has yet to happen.
Of course, never leave a child unattended on the veranda. If you have little monkeys, people have reported having the veranda furniture removed (although why you'd then pay for a veranda, I don't know).
If you are really worried, get a room with a porthole.