Although I can see your reasoning in your answer, the only thing I've found detailing any of his military experience says:
Aware of the positive effect of military service on his father's political success, Franklin Pierce saw an opportunity in the Mexican-American War. He helped enlist men into the New Hampshire Volunteers and was himself a private. Using his connections, he appealed to President James Polk for a commission. The President repaid Pierce's old campaign favors. By the time the force sailed for the Mexican shores of Veracruz in mid-1847, Pierce was a brigadier general commanding over two thousand men, though he had no military experience whatsoever.
It goes on to tell about battles in Mexico, his fall from his horse that crushed his leg, causing him to pass out from the pain, and soldiers who (perhaps resentful of a purely political general) referred to him behind his back as "Fainting Frank". The wording in the paragraph I quoted, however, indicates he received his commission as a private, although I could be wrong.
I've done a lot of research on this, and I'm starting to think it was a BS question, the answer to it being "No former US president was ever an NCO, although President Buchanan was enlisted, and President Pierce began enlisted and was commissioned."