Officers on the other hand can’t be drafted. An officer must take the oath freely and without reservation – under penalty of law. If it turns out you, as an officer, are unable to well and faithfully execute the duties of your office because you have mental reservations which you kept concealed at the time of your oath, then depending on the circumstances you’re likely to face resigning your commission or sitting in front of a court martial on your way to prison.
And the creator of M*A*S*H talked about his experiences being drafted, and how he came to create M*A*S*H, but doesn't say what the process was.
Doing various research, I've turned up various interesting items, but none that precisely answered the question. For instance, at one point (possibly the Vietnam war?) doctors who had part of their medical-school costs paid for by the U.S. government, were eligible to be called up - not quite a draft, since they presumably agreed to the payments.
It's also possible that the Oath of Allegiance that officers took, was different earlier - I found one reference to it "taking its current form in 1959", and don't know what the earlier form was. I also found references to an Oath of Service as an alternative oath, but in the context of non-U.S. citizens.
So what was the situation, then? The doctors were clearly officers, not enlisted (who can be drafted). Were they required to take an oath "freely, and without reservation"? Or no oath of any kind? Everything I can think of, is problematic in one way or another.