I think it depends on the horse and what they know when you start out with them. I once got a 10 year old QH mare that was a speed demon- she could do any pattern in her sleep. But by the time she came to me, as soon as you led her to an arena she'd get all kinds of worked up. You could try for hours to calm her down and simply get her to walk in an arena to no avail- get her out on a trail and like a flip of a coin she was a lazy pokey lady with head hanging low.
I would have never been able to make her into a WP horse just from her understanding of an arena that had been drilled into years prior. That said, I'm sure depending on the horses history and trainability paired with very clearly changes of tack mentioned above, you could swing it.