In response to your question, yes it is possible to take off time after graduating from medical school before residency or to take off any time at all, you are still free to do whatever you like. However, what effect the time off has on your residency app is another story. If you take a break before med school, you probably won't be asked a lot about it. If you take a break during medical school and spend the year surfing in Hawaii, some residency programs will question your dedication towards medicine and that might hurt your application. If you take a break right after graduating from med school, the same thing will happen except then I have heard that they will also assume that you applied for residency and think that you did not get in anywhere your first time. I have read that some residency programs consider research to be the only worthwhile activity to take off from medical school to do, so if you take off time during medical school to do that, the opposite is true and you may help your application for many residency programs. Many students do this if they are going for competetive residency programs, some between 2nd and 3rd yr and others between 3rd and 4th yr. I don't know what residency programs think about taking time off to get another non-research degree like an MPH or MBA, but I would imagine that primary care residencies or preventative medicine residencies would like the candidate with the MPH. I don't know which programs would like to see candidates with an MBA, but I can't imagine it hurting your application much either (unless a program director hates business people, which some do).