Perhaps McCoy didn't need to complete a full course load at the Academy at all.
IRL, military doctors don't go to the service academies, but receive commissions at - I think - the O-3 level. (For instance, my dad served in the Army Medical Corps, but didn't go to West Point; he was commissioned directly as a Captain when he joined.) Perhaps something similar applies to Starfleet doctors.
True, we see McCoy attending classes and taking the Kobayashi Maru
test with Kirk, but that doesn't mean McCoy has to complete a full curriculum like Kirk is doing.