OOO! I can actually answer this one! 
I went from decent English on-the-flat to jumping badly to barrel-racing to dressage to reining to dressage to jumping even worse back to dressage and now I'm learning WP. I can tell you that reining and dressage have almost the identical seat. The cues are similar as well. Barrel-racing isn't far off. I haven't actually done WP long enough to say I know how to do it, so I can't speak to that.
All that said, I'd say if you've got a decent seat and good balance it doesn't much matter which saddle you ride in. The dressage saddle feels to me almost identical to my barrel saddle in terms of where it puts my legs/seat/back. The devil is in the details (and the funny clothe), not the saddle.
In addition, I've seen dressage horses improved by pole-bending. My mare learned her tempi changes bending poles bareback. It all works together.
Go for it!