I recently finished an online MHA while in med school. It all comes down to time management and what your end goal is. Some programs are great to simply get 3 letters after your name, others really teach you business and healthcare principles (typically harder). It may or may not look good on a residency application, but more than likely, after medicine you will be able to use it during a job hunt. The bottom line is you need to figure out why you are getting the degree and what your end goal would be. If you want to be able to run your own practice, some online programs aren't going to be as good with getting you the know how.
Other online MHA programs are quite good. I ended up transferring out of one program after the first quarter because it was nothing but 8 discussion posts which didn't really need to relate to hard business principles and then a paper that I'm pretty sure the professor didn't even grade. I might have put in an extra hour of schooling a week. The current program offers more structure and more focus on actually learning business principles. If my goal was simply to get some extra knowledge and put it on my CV then the first program would be better because it didn't require as much time learning actual business practices.
I think it depends on the mentality you have and what your stance in regards to med school is like. Simply loading up your plate with extracurriculars might look good on paper but most people are able to realize that you are doing it only for a resume builder. I think it is doable as long as you make time for it and it is something you want to do. I really enjoyed the reprieve I got each week by switching from science/medicine to business ideas.
