There's no way Yusuke could win this fight. From what his feats show, I'd put him on Goku's level when he's fighting frieza before he goes super saiyan. However, at the end of YYH, it's implied that Yusuke has become nearly all-powerful.
Actually, what would probably happen is that Vegeta would beat the crap out of Yusuke and mock him relentlessly, and then Kuwabara would show up and be like, "Hey! Urameshi! Come on! You can take this guy! Ya gotta! It's what men do!" And then that song called Struggle for Sorrow (which may as well be Kuwabara's theme) would start playing, and then Yusuke would get up keep trying to fight, and Vegeta's punches would suddenly be slower for dramatic effect, and then Yusuke would get knocked down again. And then Kuwabara would get mad and attack and get beaten up too. But then Yukina would show up and Kuwabara would cut Vegeta's head off.
That's what would happen.