One additional question with regards to the above, though, if I may:
Does this mean it's not intended/possible to register ldap instance(s) on machine A with the config-server on machine B? I assumed it was because answering "yes" on the register-with-existing-configserv step in setup-ds-admin.pl prompts you for a full ldap-URL.
You usually have a single configuration directory server for a single admin domain, which may consist of many machines. So yes, that's what that dialog does - it registers your directory server with a (possibly) remote configuration directory server, used to store configuration for many machines.