From NC State's NROTC Website: "Before offering advice on the college/university placement section, I will take a step back for a moment to familiarize you with how the whole process works. Scholarship selection boards for the Navy meet about a dozen or more times (depending on the total number of applications) throughout the year with the first board usually convening in late August/early September. Marine Corps scholarship selection boards are held in November and February. Each board will review approximately 500 applications and they are reviewed in the order in which they are received. For this reason, you want to make every effort to have
all of your application complete by
early August so that you will be reviewed as early as possible. By August, there are usually 2,000 to 3,000 applications completed so if you’re just finishing in the September timeframe, you may not be reviewed until several months later. The selection board "scores" all of the applications it reviews based on everything contained in the application and then selects the top hundred or so highest scoring applications. Those not selected are automatically rolled to the next board which would meet about a month later and select another hundred or so applications. In this manner, about 1,800 to 1,900 students will ultimately be selected over the course of the year (the last board meets in April) out of the roughly 8,000 to 10,000 that apply. This represents around a 20 percent acceptance rate, though it varies by year. Again, this is why you want to take the time to make your application as strong as possible. "
http://naval.dasa.ncsu.edu/general-information (see pdf file "scholarship application - helpful information")
There are school units that fill faster than others however I can't speak definitively regarding that. Search for posts from Pflying-17 who used to be active here and was an "insider." She noted some units that filled quickly and others who normally had openings late in the process. Of course, the information will be dated. Also, there is a request process to transfer the scholarship once it is earned.