Won't work. It's a volunteer, unpaid position. They have no legs to stand on in this case. The only real course of action they have is just not giving Reddit their service at all. Stop going there, stop giving them clicks and traffic.
Good luck to them. I dislike Reddit as much as the next guy, but this whole thing doesn't stand a chance. You do volunteer work nobody even asked you to do and then demand money? How does that make any sense at all?
I don't think the point to to actually get paid. I think the idea is, as you said, media attention, as well as investor attention. Who's going to want to invest in a company that's trying to unionize?