Earlier quoted context omitted.
Of course not! If they cared, it would be handled or they wouldn't use consultants.
I'd put a caveat on that where they care if it makes them look bad. If it's readily apparent that your patron dropped the ball in prep (either through incompetence or simply ignorance), then that can be a very bad round of the blame game. This is where providing transparency and insight (in a "how can we fix this?" way) up to management can help engagements go more smoothly. If everyone was aware from the first that…
I wouldn't advise to participate in the blame game or to point fingers. You are not here to cause troubles and trouble is bad for repeat business.
P.S. Organizations are dysfunctional and the majority of consulting time is wasted. Lesson one of being a consultant is to live with it. :D