Could they, sure. Would they be very good at it or place very well at a show? Not likely.
They are a gorgeous, wonderful breed of horse who was designed to have a smooth, ground covering natural gait. Part of their gait is their "termino" or the sort of paddling motion that they do with their lower leg from knee down which can be fairly counterproductive to jumping. As someone else said, it also comes down to the individual horses conformation as well.
For the amount of money a good registered Peruvian will cost you, you would be better off getting another breed more suited to jumping if that is what you really want to do. I know in my area a young Peruvian just started in bit goes for $7,000.