If they win against you... well, I suppose they'd be Champions and you'd just beat them all over again. Or maybe it could, again, like the Battle Frontier where you can keep track of how many trainers you defeated as your were Champion. Interesting way to look at it, and maybe you could see how other Champions fare, like if you check it on Wi-Fi on global chart, or just in-game trainers, like Cynthia reined for 800 battles or something.
I love the idea of the dungeon Champion thing. Steven was hard to get to, just as much as Red, and their battle was so fun. It'd be kinda funny if Champions roamed around like roaming Pokemon and the TV would keep track and you could just stalk them and battle them. Or just a dungeon. Either way, re-battling Champions when they're better sounds a lot better. I wish other people recognized you more, though. There are a few people in the trainers' club and other places, but most people just repeat the dialogue and aren't head-over-heels to you like they are for other Champions. Eh, that's really trivial xD