Yes, they certainly do read the statements. How closely and carefully will obviously vary from one place to the next.
You don't mention what field you are in. I'd say that the tighter the market, the more these application parts matter (the more qualified applicants there are competing for any given job, the more necessary it is to find ways to eliminate candidates). As a rule, you should assume that if they have any interest in your candidacy, they will go through every item in your application with a fine-toothed comb.
Good luck with your search!
Invisible Adjunct
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