Starting med school in a couple of weeks. We don't have mandatory attendance for 1st and 2nd year so, i'll have time to run. I'm only aiming for about 30 miles a week, just enough to stay fit. I've heard stories of people doing a run after a 30 hr surgery shift but I don't know if I can do that.
Haven't started med school yet myself, but a friend of mine just finished third year and has been able to run consistently while performing very will in school. I think it just depends on priorities and discipline. Are you the type who can basically do nothing but run, work, study, and take care of hygiene/biological necessities every day for a year straight without much of a break? Then you can probably run way more than 30 miles per week. Are you the type who needs to crash in front of the television for an hour every night to unwind? Then running will be tough.
Third year will be toughest. Fourth is generally a bit easier, from what I've heard. But if its a priority, you can do it.
Med school is not that hard or time consuming. People in med school just exaggerate it so that other people are impressed. I for one am not impressed. You should have no problem running any mileage and will have plenty free time too.
You can run, and 30 mpw might be very realistic. Much more would get difficult when you start having rotations on an irregular schedule, and with studying in between rotations. But I've known people who train moderately while in 3rd and 4th year.