I don't think any marine will have COC. When you join an organization like the marines you are actually giving away your spirit as a ruler which goes completely opposite to the freedom of the pirates. I think only the very top like tenryobito or the Gorosei would posess the COC.
The COC has never been directly tied with "freedom", that's a characteristic mostly associated with the Will of D, which as far as we know is something different. The fact that multiple "D's" have joined the Marines, also shows they don't exclude one another either.
The COC one the other hand has been defined as the innate quality to rule over others, which doesn't automatically equate to freedom. For example Dogtooth might be a pirate, but he sure is on Big Mom's leash. In fact BM's crew is so hierarchical and strict that something like freedom is non-existing. It's Luffy's philosophy that a real pirate is someone free, but that's not a universal thought. In fact it seems to be a rather unique concept. Likewise DD might have been a pirate most of his life, he however was born a Celestial Dragon and even tried getting back to Mariejois. He didn't become a pirate because he wanted to, he was forced to.
Also rationally speaking if you would have the drive to "rule", it would make much more sense to join the Marines and/or the World Government than doing something else. As a whole the WG is the highest and most influential organization in the world the likes even the Yonkou can't match. Meaning the higher you would climb up into their organization, the more power you would gain over the world itself and the more...freedom. This is something Smoker specifically mentioned and Garp's and Sengoku's antics also underline this. Why bothering creating your own ladder when there's already an existing one?
The COC is neither good nor evil. So any sense of morality a wielder might have, will be derived from his own personality and experiences. Meaning for example someone who has a strong sense of justice and wants to rid the world of evil, will have a strong urge to join the Marines. Hence I believe Akainu is a strong candidate of having the COC.