In general, no they won’t update you in the middle of the cruise. If you think about it, everyone reaches their threshold of points in the middle of a cruise. Or nearly everyone. The odd person might hit the right number of points on the last day of a cruise but the vast majority get to the required number of days/categories in the middle of a cruise. That’s why they don’t change your tier level until the cruise is over.
The back to back passengers who achieve the new tier at the end of cruise one just don’t have to wait the usual 7-10 days for the points to be added to their account. The Captain’s Club host can manually advance them to the new tier for their second cruise.