Unless otherwise already gained a promotion due to other merits.
ie Uhura, Kirk and in a slightly different scenario McCoy.
You can't gain a promotion until you have rank. Cadet is not a rank. You don't get rank until you graduate - when you become an Ensign. You don't have rank when you're in training. That's why they call you cadet. Because you don't have rank. It's the equivalent of calling an enlisted person who is in training a recruit. When you don't have rank, you can't get promoted. It's impossible.
Take it from someone who's spent a decade in the military. Trust me on this. I know what I'm talking about.