a cadet outranks an NCO? Can anyone who was actually in the military weigh in on that?
When I was in the Army and was briefly in a commissioning program I was considered a cadet and was treated like a regular officer in many, but not all respects. My pay grade was actually that of a sergeant though.
In Starfleet's case, I think it would depend on how the Academy is geared toward producing officers versus enlisted so I can't say with any certainty either way. If O'Brien ended up on that ship, I think he'd still put Watters in his place somehow.