True, Aikikai Hombu dojo doesn't regulate kyu grades. So, aikido organizations and dojos can do pretty much as they please with them. Some dojos might even decide that you have to take the kyu grades all over again, when you transfer from another dojo.
My guess, though, is that most Aikikai dojos respect kyu grades given by other Aikikai dojos.
In most cases, overseas organizations issue kyu ranks locally, so other organizations may or may not accept them - I also know of organizations in Japan that do the same thing.
Some organizations in the United States (even some in Hawaii) have their ranks issued by Aikikai Hombu starting with the kyu ranks. In that case I would expect that most other Aikikai organizations ought to accept those ranks - although I know of cases where that has not happened.
Basically, my experience has been that Aikikai dan ranks are accepted at other Aikikai dojo, but with kyu ranks (whether issued through Aikikai hombu or locally) it depends on the new organization.