I don't know what the book says about a child outside the wards. Or- well, there was one recently in Ireland. Since the new wards went up, but perhaps Ireland is still considered within the book's territory.

I wonder what it said about Mr Finch-Fletchley. Or was he born here?

If a child dies before coming to school, the book annotates its entry: '(dec.)'

I don't know what would happen if a magical child were stillborn or died before it were named. That's a possibility, I suppose.