Would there be two kid Buus if the Kai was removed from Fat Buu?

Ok, so I remember this part where Vegeta threatened to remove Fat Buu from Super Buu and he was all like, "No I wouldn't be me anymore!" So Vegeta did it, thus Kid Buu. But what if Fat Buu got that Kaioshin taken out? Would he be a Kid Buu, too?
I'd 愛 to hear your thoughts on this, people. :)