well, it depends on the horse. a well bred(uncrossed), well trained walking horse will not trot, the have a variation of walkes and canters, but none are actual 2 beat trots.
as for other breeds, like the fox trotter has a gaited trot.
so yes, technicaly, all gaited horses can trot, but, like the walking horse, they are trained and bred to do a certain gait.
i have a fox trotter, a saddlebred/paint cross, and my grand parents used to breed walking horses. also my mother used to have a morgan horse.