I doubt that Monks cares about the lax boys charged with rape. I think he sees the entire episode as an opportunity to sneak himself into this particular elective office. The lax boys are as much a campaign tool for him as they are for Liefong. At any rate, he's deluding himself and is nothing more than a spoiler. He's also an idiot because he's going to end up being the most reviled man in Durham County if he splits enough votes away from Cheek to cause Liefong to be elected.
I doubt he is dumb enough to think he has enough support to sneak into that elective office. I really don't know what his motivation is, but I doubt even he thinks he can actually be elected.