Yes, but at least in the USAF they are registered with the USAF. I'm assuming that is like this in other organizations as well.
I have seen my sensei accept kyu ranks across organizations. We had a visitor for about 6 months from South Korea and my sensei recognized his third kyu. (He was very good btw and we all loved training with him.) Although, his school in South Korea is affiliated with the Aikikai Hombu.