Duffy, from my experience the progress truly depends on instructor, not so much on horse. So if you find a good eventing or jumping instructor I'm positive you could do it. My dressage trainer while she jumped too years ago told me on spot that she won't teach me jumping, because it's not her specialty. I'm taking lessons with the eventing instructor (who is very much like my dressage trainer in her teaching and approach, so it works for me).
You have NO idea lol, every time I jump I freeze.. even if the horse jumps well, I generally fall off because I've frozen from fright
I'll look in to it when it comes, going to free jump her first to assess what she does ( I am not getting if she's a nutter) and see how we go... even talking about it makes me feel sick to my stomach!