The reverse of yesterday's question.
It depends - on whether the carriage horse is trained to ride. One thing worth noting is that people who owned carriages often did train the horses for riding as well. This was particularly common in the 19th century - Black Beauty, Ginger and Merrylegs were all trained to both ride and drive. It was a lot cheaper to dual train a horse than have separate horses.
If the horse has not been trained to ride and somebody tries that, they're likely to get bucked off. If the horse has been - then yes, you could do that stunt. If you knew what you were doing and had rehearsed it with that horse - otherwise they might spook and run away without you.