As a somewhat relevant example, the newly minted "Senator" status for those who participated in the status match is reflected in the Lufthansa systems, but does not (yet?) work when added to bookings on the other *A airlines. I assume there is a "data broker" that allows lookups by the FF number, and that still has not been updated. In this case we are talking about a new number in an existing (and, thus, properly integrated) FF program.
I am guessing that integrating the *entire* program will take longer than getting a few accounts updated, so - very unlikely that anything will be working from "day 1" (and I'd be surprised if things are smooth enough even in 1 month, especially given the fact that SK still provided no information on what exactly will be happening)