... or even after! My dad got drafted in 1961; he was given 30 days to report to the Army. A buddy of his told him that one of the "good reasons" that you can decline to show up is if you are already a member of the armed forces. They went downtown together that day and raised their right hands for the Navy. My dad spent two glorious years sailing the southeast Atlantic, visiting Rio like, well, like a drunken sailor :)
I don't know how long this loophole existed, but I get the feeling that it went on for some time (if not until the end of the draft).
/jordan