It will. But it is hard to recocnise the duration has been shortened if you have no idea how long its been originally. Thats why i gave the example. Without upgrading your doc a 2 week, 13 days injury does not exist...at least i never heared of it.
We are talking about 1 or 2 days which is small compared to the influence the doc has right at the time the injury occurs when he can make a 2 week injury at lvl 1 just for the match at lvl 4 (just an example) which is like 17 days shorter.