I imagine if Pokemon became real in Arlen Bobby would be the first to catch something (probably a Clefairy, Togepi or something else cute), which Bill would take an interest in it but hide it from Hank, Dale and Boomhauer. Hank would obviously look down upon Bobby's training but, because of Peggy, be convinced it was just a phase he would grow out of.
Eventually Dale would find out about Bill's secret and make a deal that he wouldn't tell Hank if Bill gave Dale one of the Pokemon. In the meantime Hank would adopt a Stoutland from the pound with Peggy's encouragement, thinking it's just a regular dog and hoping it could help Bobby realize how weird Pokemon are and how nice it is to have a regular, American pet.
When Bill and Dale's cute Magikarp evolves into a Gyarados beyond their control, Hank's Stoutland tries to stop it to protect Bobby but is injured, leaving Hank confused and pissed at Bill and Dale. Boomhauer steps in and uses his team of fully evolved strong Pokemon to stop it, having already taken up training before even Bobby.
And that is what would happen if there was some bizarre King of the Hill/Pokemon crossover.
