As I understand it, you are still an undergrad. So, you are not yet a Navy officer.
Therefore, I think it is premature for you to be applying for a grad school that isn't going to happen for years.
One of us is having a misunderstanding.
Either you are going to join the Navy as a nuke officer, or you are going to grad school. You can't do both at the same time. So, my question is; in what order do you think you will be doing these things?
If it is the Navy first, then grad school is years away. You'll go after you get out, or you'll be a career officer and go when they tell you you can. Either way, it is at least four or five years away.
If it's grad school first, why? The Navy doesn't actively look for people with post-grad degrees in nuc. eng. Most nuke officers are ME's or EE's with a BS degree and impressive GPA's.
Talk to a nuke officer recruiter before you get too far into this process.