I am absolutely certain that they do, and over thirty or more years of careless applications will have made it so.
Obviously the reason that your essay for Why MBA? being similar is not lost on them, and it ought to be compelling irrespective of the school you apply to.
For example on the carelessness that takes place, I got an email perfectly addressed to me, with my background correct and other items (I was on the websites as a contact). I was asked how my experience was of UCLA Anderson, and any regrets that I had.
My email address? email@example.com
(that will reject, so don't bother - it was illustrative)
Given that my name was provided as an admissions contact goes to show how many slips get made, and it does happen on essays (we were encouraged to warn about that every information session).
Would it seriously impact someone's candidacy if that mistake were made in an application? Perhaps not so "illustrative" as the one you mentioned, but you can still sort of tell. How can you avoid falling into that trap?