It is curious to me why GCHQ didn't just contact GitHub to acquire github.com/gchq but instead decided to go with the long and cumbersome github.com/GovernmentCommunicationsHeadquarters. Perhaps it is a British thing [1].
I'd say they definitely have the skills to acquire it, if QUANTUM {INSERT|DNS}[1] are still operational. As you said, it's probably not worth it.
1. http://blog.fox-it.com/2015/04/20/deep-dive-into-quantum-ins...
> Account names may not be inactively held for future use. GitHub account name squatting is prohibited. Inactive accounts may be renamed or removed by GitHub staff at their discretion.
I have been able to acquire a couple of GitHub names that have been inactive for several years by contacting GitHub support, and they usually reply within a day or so.