FYI, I had hoped that perhaps we could register him after Jan 31 if the worst came to the worst. Not being sure, I've read up on the rules and it seems that is not the case. The transfer window is an opportunity to apply for (amongst other things) "the registration of a player transferred to it".
Outside of the window, the Board can refuse an application for a registration, or grant it - possibly subject to conditions. Since this is City we are dealing with, that means refuse it.
Sorry if this was obvious, but to me it was not. I had imagined that since we had signed him already, the registration could perhaps be done any time (as is the case with players out of contract).