I was working on healthcare projects at Mckinsey for 2 years and I know the folks who came to McKinsey with a pure medical background.
Application process: While medical background + MBA is a good fit, non-top school may be a problem. Big 3 companies are hiring most of the guys from the Top schools. Two hints here:
One hint that may help you - try to contact your classmates who worked at Big3 companies before MBA and ask them to recommend you. For example, at Harvard, McKinsey only invites for the interviews the guys who are recommended by classmates. It's not a referral in most of the cases. Big3 HRs are just in contact with their employees pursuing an MBA.
Alternatively, you can get a referral from current employees, but that only works if you are applying full-time (does not work with the summer internship). Tip: it will be easy to connect ex-doctors and current McKinsey employees on LinkedIn and get their advice and maybe even help. More on the referral here:
Interview process: for these candidates interview process was the same as for other candidates, thus you should be well prepared for cases and fit
Work experience: While healthcare projects went for them pretty smooth, I saw the guys struggling with the other industries. Unfortunately, you have to make this transition to get exposure to other teams and partners. Thus I recommend you to have the first projects in healthcare, get all the necessary skills and then gradually and very accurately increase your exposure to other industries.
Guys with medical and consulting background made probably the best exists from McKinsey I've heard of. Even though some of them were underperforming at McKinsey. On the contrary, if you are doing healthcare and have no medical background the exit opportunities will be limited