To be clear, when I say dressage, I'm not referring to what saddle you're using, what clothes you're wearing, the horse you're riding or having a trainer with a German accent.
I have attempted dressage in a western saddle. THAT was an exercise in futility. I felt like my normal, concise aid of "please bend around my inside leg" turned into "ghhmghfffff!" by the time it got through the damn saddle. Maybe that was just my lack of skill as a rider. The mare did kind of understand but it took a lot more effort on my part. If someone else wants the added challenge of using a western saddle while doing dressage, they are more than welcome to it. We use the tack we use because it helps us be more effective, not because of what it looks like or because that's the only thing that can possibly work.
I've done a few really low level jumps in a dressage saddle. But if I wanted to really begin jumping, I'd at least borrow a jumping saddle.