I just speak from my own searches about CTN and all, but I do not think CTNs program, at least not much if they do. The only thing I have found on "Navy programmers" is that this would be taught at a place like the Naval Postgraduate School for technical officers. CTNs have more to do with global networks and cyber security. And "within a short period, today's CTN quickly develops highly marketable computer skills" something that the other rating cards do not say about their respective ratings I've noticed, so I would say yes.
https://www.cool.navy.mil/enlisted/r..._cards/ctn.pdf