No, Vaughn doesn’t want children. A person in his position usually would, for the reasons you’ve mentioned, but Vaughn has the ego of a true psychopath. He doesn’t care what happens to his business or his fortune after he dies, or about continuing his family line, or anything like that. As far as Vaughn is concerned, when he ceases to exist, so will the rest of the world.
That’s fortunate, because I agree that the idea of Vaughn anywhere near a child is horrible! The only sticking point he’d run into is that he makes a concerted effort to present himself as a “normal” person, so he’d probably catch some flak from society for not having kids. But he’s still pretty young - and a man - so he hasn’t encountered that situation yet.