ADad,
At Army, they have the (I think it's called) Pro Service Option. They will allow their athletes to go to pro sports, either through the draft or free agency. Their first two years of pro play, they work off seasons as an Army recruiter. If still playing after that, they owe the Army a specified sum of money for the education (which the baseball coach explained that the pro team pays), and take your remaining three years of active duty, double it to six and place you in the reserves.
I have come to find out that all the academies have different policies, this one is Army's. So the long answer to your short question is, yes, Nick Hill can go play pro ball if he so desires (along with Milan Dinga). There have been two Army baseball players that have gone that route since enactment a few years ago.