For what you want to do then, an MBA certainly could, although I have my doubts about JHU's MBA program getting you there.
Consulting firms are very pedigree oriented, so you are best off trying to get into the best school you can (ideally a school ranked in the top 16, but at least in the top 30). If you want a 180-degree transition, a full-time program is the way to go. However, you can also get a part-time MBA, keep your job with an eye towards a medium-term transition (i.e. within 3-5 years as opposed to 18-24 months or so with a full-time program) - that's a personal decision.
As for the other types of grad programs (doctorates and master in public health), I really have no idea. If you're going for a business-oriented job function (finance, consulting, strategy, operations, etc.) in most industries, the MBA is the way to go.
Alex Chu
alex@mbaapply.com
www.mbaapply.com
http://mbaapply.blogspot.com