That's a true statement. But you also neither need nor should ask a bunch of guys who've never held the roles you're asking them to hold, to spontaneously build a new skillset. The folks that have been NCOs should be NCOs, Warrants - Warrants, Officers - Officers. And then whoever leads, leads. Leadership isn't about who has rank, it's about who gets things done. Putative leadership is absolutely about rank, and should be.
Rank, particularly in that scenario, can be a great hook to develop a character around. Spontaneously deciding that the investment the character made in that rank (or the investment the dice made for him/her) is worthless because the characters are in a mercenary unit now doesn't make a whole lot of sense. If the character with the rank screws the proverbial pooch, then it's on his head (and that means both in terms of tactics and in terms of dealing with his partners/minions).
It's not my table, but the OP asked, and I'm answering. Let the guy who mustered out with rank, retain the rank when entering the mercenary unit. If the other players take issue with that, you can resolve it at the table and let the character with the rank work through those problems. If it proves too much, then you resolve it with fiat.