Maybe Kaido found some answer in Wano when it comes to Joyboy before ultimately giving up on that idea, but if it was due to his fight with Oden then that would be trash, nothing in that "war" indicates that.
To King it didn't matter if he was or wasn't he was still gonna follow Kaido, he respected his strength, he wanted to make him PK, he believed Kaido was joyboy but if he wasn't he wasn't gonna turn on him, most important Kaido didn't sell him out.