It's certainly possible, and it makes a lot of sense. One could maybe make the argument that its "against the spirit of the agreement", but Dalinar specifically said he'd be his own, so that's a tough sell. And it definitely makes the most sense, its a very "safe" option to more or less guarantee a win. I doubt Rayse would have done it because of pride, but Taravangian probably would not care.
However, it just doesn't seem right to me, narratively. Yes, the two characters are obviously foils, but fighting directly against a shard is a pretty hopeless fight. And since Dalinar will probably lose, it just seems like a kind of weak ending to this first arc. Plus, when Taravangian was thinking over the agreement, the way it was written, it sorta felt like he was going to do something really smart to deal with this situation, not just vaporize poor Dalinar with the full power of a shard. Though, perhaps there are some restrictions on Shards fully manifesting in the physical realm? Maybe that would make it more fair?
I think this could work if Odium was still pretending to be Rayse, then says Taravangian is his champion. Dalinar thinks it should be an easy fight, at least in a physical sense, and its only after the fight really starts does Dalinar learn that the fight is hopeless