If you join the navy as a nuke, any plans to complete another degree, or a graduate degree will need to be put on hold for the next several years or so.
NPS is a full-time job, followed by prototype, which is a full time job on a rotating shift. Then off to the fleet, where you'll need to get qualified the basic watches (EOOW/EDO), not to mention OOD after that....at this point you've been in the navy for 2 years or so. Spend some time learning the different jobs at your seagoing command, then off to PNEO and the engineer's exam. All the while, going to sea for anywhere from few days at a time, to 9 month deployments. The good news is, the sea time gives you ample time to study by immersing yourself in the study material.
That said, stick with it long enough, and the navy will pick up the cost of your graduate degree.