Yes, most...if not all states do have a process for securing title for a "custom vehicle". For instance, any time you have/make a motorcycle with a VW rear-end, which is pretty common...that's a custom vehicle.
you can get VIN's easier then you'd think. Plus there are many ways to do it because of the people that built many other kinds of kit cars such as cobras being a prime example.
However, the real question is whether or not the guy has any knowledge of vehicle dynamics and how well the thing will drive/handle/perform or even be safe.
He should contact the BBC to see if he can convince them to transport him and the car to the Top Gear Test Track to compare it to an original. (yes, I am aware that there will be a US knockoff version of Top Gear full of Michael Boltons)