Though I haven't "been there and done that" myself, I do have several colleagues who successfully switched from IT to MC - however within the same firm. This may not be the route you seek, but they essentially joined the technology side of our firm with the intention of switching into MC.
I'm not familiar with Said, but having a strong resume and acing the case interview will land you an MC internship, if not a role. If you're already preparing for case interviews, that's great. I would do research and see what MC firms recruit at Said. Going through on-campus recruiting will increase your chances of getting an internship / job because you're generally guaranteed an interview. Your background won't prevent you from switching into MC, but without an MBA, you may be stuck with an entry-level position.