Well, I disagree with the above poster but I can see his point and respect his experience.
The MBA is a valuable tool with no business experience, although I personally think the experience is enhanced if you already had some coursework or work experience (which is why many schools require it). With the right classes you learn the basics of "business" from finance, marketing, economics, statistics, accounting, organizational behavior/HR stuff and most of all critical thinking. Every school has its own format on what their focus is. I often wish I would have gotten more out of my MBA because if you choose to really get involved in the coursework there is ALOT that you can learn. I can honestly say that I had some doozy of professors but I learned A GREAT deal in my program. Its not a Top 20 program, or even a top 50 program. But its gave me a solid foundation and is a highly regarded school in the regional area.
MBA programs are different line of thinking if you've never had business classes. I've had a few people I know say they spent more time studying finance than they did for some med school classes because not everyone can "change gears" as there is a different thought process involved to some extent.
If you have an interest in business would like to maybe move into health care administration or have options later down the road (private practice, get out of medicine) I'd suggest the dual degree. Its also great for just understanding general business in life as well. I really am a huge advocate of people understanding basic accounting, finance, etc. You'd be surprised where you might end up you need it.
So that is just my opinion but if it doesn't cost you anything and its a decent program, why not? Ask the program to put you in touch with former students and current students. Ask for a few of them. Try to contact them and see what they say about the program.
My vote is go for it because I am a person who likes to have options and I plan on using my MBA in MANY different ways. Its nice to have a different perspective on things.