See, that wasn't so hard was it?
So, given that it's binding once signed, that means it could be announced straight away. The registration stuff just means the player can't actually play until that's done (which is usually a matter of hours not a week).
I get the media team bit, but again, a week seems excessive.
Clubs have players who sign a contract on a Thursday night or Friday morning, are registered and announced then play on the Saturday.
As said, it was a simple, genuine question. I don't think you actually know the reason (because what you say doesn't stack up), but just want to sound like you do.