When they install the new Windows 2000 server, it won't be a BACKUP domain controller, it will be a domain controller, of equal status as the existing w2k domain controller.
Windows 2000 Active Directory setups do away with the idea of primary and backup domain controllers that NT4 used to use. All domain controllers then become on par with each other as they all have the Active Directory information replicated to each of them.
What I would think they should be aiming for in your case is to first bring online the new w2k domain controller and make sure that is running correctly.
When you are happy with that, you can upgrade the NT4 box to a w2k domain controller (pop in the CD and it should do it for you).
Once it's up and running as a w2k domain controller use DCPROMO.exe to 'Demote' it from Domain Controller to a Member Server. Since you are upgrading in place you shouldn't lose any info on it, just make sure the computer meets all the windows 2000 requirements and isn't going to fail the upgrade due to old hardware/incompatible applications installed on it etc before you start the upgrade process.
And finally switch over from running the Active Directory network in 'Mixed Mode' to 'Native' mode to say that you no longer have NT4 domain controllers in operation.
Sorted!