1. Best of luck with the board.
2. There is no way that you will have the time to get a masters while on Sea Duty as a SWO, especially one as intensive as an engineering degree. Furthermore, you would need a Masters of Science not a Masters of Engineering as the community does not consider an M.Eng. to have enough academic rigor. There's no way that that's happening on sea duty and very improbable that you can complete it on shore duty. When you get to the ship, your focus needs to be entirely on getting your SWO pin and learning how the Navy works.
3. The curriculums at NPS are tied to a specific subspecialty code and cover specific topics the Navy deems necessary to do your job as an EDO. You need to have one of these subspecialty codes in order to progress through your career. That being said, can you get an equivalency waiver for non-NPS or MIT coursework? Yes. Is it difficult? Also yes. But it can be done and I know one or two people who have done it. It's rare and requires the OCM to do work on their end. It's also very curriculum dependent. What's your masters degree in? If it's not a hard engineering field (Mechanical, Electrical, Civil, Systems, Industrial, Aerospace, or Chemical, also Physics) then you're likely still going to have to go to NPS.
4. Will it help your chances? Maybe. The EDO community fully expects to need to send you to NPS to get a degree that they see a need for with classes that are very Navy-centric and will help in your role as an EDO. I know a couple of guys who came in having already started their masters work with online or night classes and they got nothing out of it (no transfer credits or curriculum preference). I know a few who already had masters and still had to go to NPS.
5. Why would you give up the option to get a 2-3 year tour in Monterey, CA, where you get paid to go to school full time at one of the leading research schools in the country? You do yourself a disservice for trying to get out of that.