I'll second that it would be an advantage, though a small one, when applying for residency. It's clearly not worth it if all you're trying to do is improve your match chances.
I'm not attending at an EM program, but during my senior year I had some chief resident duties which included interviewing and evaluating incoming applicants. Judging from that limited participation, an MBA would have been an "interesting, but not a deal-maker" kind of feature on an application. It might catch an eye on initial review, but unless there was some real world experience or ambition behind it, it would eventually be a non-issue. Would it improve your chances for getting an interview? At my program, I'd say it would be a very qualified maybe. Again, unless you had a good reason and or experience for that extra degree, then at the interview it would either be discounted completely or even thought of as flakey (for getting a degree for no good reason) by some of the less forgiving faculty members. We didn't have quite that situation come up, but some similar things on applications that left us scratching our heads. Being labeled "flakey" would decrease your chances of interviewing, immediately put you way down on the rank link if interviewed, or even put you off it completely.
So if you have a good reason to want the MBA, then by all means do so. If you're just CV-padding, don't bother.
