I don't see how having an additional qualification could have a significant disadvantage. You would have to pay for your courses which might burden you economically and you would always be occupied with classes on the weekends or daytime according to your preference which might affect your social life. The advantage is that almost every medical personnel has an MPH nowadays so it will help you compete on the job market at a similar level. It's helpful if you are interested in pursuing a research based career. Despite popular opinion, it's not as promising to get NGO jobs just cos you got MPH, as it's not that special of an accomplishment anymore.