Of course the career is feasible. There are programs that are specifically created to get an M.D./M.B.A or M.P.H. or M.H.A. I went to Washington University Medical School for it's health administration program and there were two students in there that were also getting their M.D. at the same time. My program was two years. They had the 2 years of business classes distributed during their 4 years of medical school. The program didn't seem difficult for these 2 students at all. Of course they were extremely efficient and geniouses, and very well respected by all.
I also know the CMO of a children's hospital that got his M.D. first, then practiced medicine. Later on in life, he got his MBA and now is the Chief Medical officer primarily using business skills but totally understands the medicine side. I did the masters in business first, worked 8 years, and now going to medical school in the fall. In the future I will have the flexibility to pick jobs that are more business focused or more clinical focused.
In my opinion, it would be wise for all physicians to get a basic concept of business because running a clinic means having to deal with employees, salaries, contracts, information systems, facility decisions, business planning, supply management, insurance, licensing, etc. Even if the clinic is large enough to have a business manager, the physician owner still gets a vote and hopefully will be an informed participant of his/her own business.
