Well, there are a couple things to think about.
1) There's such a thing as a consulting resume. They're basically powerpoint slides that go in a deck sent out to clients when projects start. Depending on the client and the project, clients will request specific people based on their resume. Like it or not, an MBA makes it more likely they'll pick you. If you get the more important, higher visibility gigs, you'll move up faster.
2) Yeah, you can get promoted without an MBA, but there is a glass ceiling. Every single partner in my firm has an MBA. That's a pretty strong indicator. I'm at the point that I'm not going to get promoted without one, and I already have an MS.