Richard
You say that BFRs will be in category 4, but the latest docs from the TSA exclude BFRs, rental checkouts and general currency/proficiency flying from "Flight Training" - so it appears that ALL FAA license holders (including aliens) do not have to register unless they are specifically going to have flight training for a new rating, when they definitely will have to go through the procedures.
That's what AOPA say too.
Regards.