Are there a combination of registry entries that a person could modify in order to modify the domain membership?
I don't think so but I don't know for sure.
Registry is local do the computer. AD is a policy generally contained in a database on a domain server that is pushed out ("enforced") to local workstations upon connection to the domain. Joining a domain involves a computer being assigned a set of policies that result in registry entries on the computer defining what it is supposed to do as part of that domain.
You can generally modify these registry entries, but they are usually reapplied at regular intervals and when the computer reconnects to the domain.
Because the AD settings are made on the controller and pushed to the workstation, they are generally one-way. Making changes in the registry will not result in those changes being pushed up into the domain policy.
Manual changes you make in the local group policy will be allowed to stay only if there is not explicit instructions otherwise coming from the controller.
According to your latest edit of the question:
...looking at what domain the computer "thinks" it is in...
On a command prompt enter:
This might answer your question. I'm not sure if this works if the computer is in some weird state.
Or in the registry: HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Lsa\CachedMachineNames
Several values contain the domain name
But to answer your original question: no, you can't change domain membership via registry only.