If Robb sends someone other than Theon to treat with Balon and Balon goes through with his invasion anyway, does Robb have to kill Theon or could he keep him alive as a potential candidate for the Seastone Chair, sympathetic to the Northern Cause?

Robb would have to think fast. Either he’d need to kill him on the spot to make it clear that the King in the North ain’t nothing to f*ck with, or he’d need to crown him on the spot and declare him the true King in advance of a future invasion of the Iron Islands.