I thought the Bearcats cancelled their NE program back in the late 90s. It doesn't make a difference for you (i.e., for the courses you need). I was just wondering.
On topic, back when I was on the Enterprise [early 90s], we had a few nuke officers with business degrees as well as a couple of history majors and a poly sci major. None of them were any worse than the rest, if anything they were a little more open minded and less rigid and pompous than the engineering majors. I'd list one of the history majors as one of the top five nuke officers that I worked with [based on plant knowledge and the ability to get things done].
That said, have you considered serving as a supply officer? I know that it doesn't sound quite as glamorous as a nuke officer, but nothing's all that glamorous once you get into it. Along with your accounting degree, some deck-plate level experience in logistics, administration, and bureaucracy could be very useful for a future in business. In most cases, logistics makes the difference between success and failure. Hannibal, Napoleon, Lee, and Rommel were all brilliant tacticians, but failed due to logistics. Don't underestimate the importance of supply to the success of a cause. In addition, the duty is far more pleasant than nuke officer duty. Just a thought.
Good luck and thanks for your future service,
mgm