The big thing is, like O'Brien who was a combat officer in the Federation-Cardassian War till he became a technician on the USS Enterprise, is that we really don't see the ground forces of Star Fleet in Star Trek. We see them here and there, such as "Nor the Battle or the Strong" in DS9. But still a rare sight, which could help explain why NCO's are not as shown as much on Star Ships.
You see the lower ranking crewmen and the like onboard the ships when they do repairs, and help with Engineering tasks. (Remember when the Warp Core was having issues in the Wrath of Khan, when one of his lower ranking crewmen who died after being given "the word" after the rest of the trainees ran). But they are for the most part skilled in something about ship functions, which tends to indicate training programs similar to current technician (Specialist) level training in militaries today.
When NCO's who are technically trained in militaries today, as they gain more experience they are often given additional training, to gain bachelor degrees in their field of work (Mechanical/Electrical Engineering) and are promoted to officer ranks. Which also explains why SNCOs in star ships are rare, as by the time they get the experience needed to be in command they are probably upgraded and promoted, as it would be a waste to allow technically inclined people to stay into lower support roles.
As for O'Brien being so old, and gaining the technical level training so long into his career, its unlikely that he would, and that they'd bother offering him Officer training. But they did end up giving him his own space station to play with, which shows that Star Fleet still considers senior NCO's as valuable officers even without a commission.
So I still think O'Brien will be able to take command of the ship from Red Squad, while he laughed at them like I did.
Jim