It may seem silly to say but typically admissions officers read the applications front to back: essay first, then the secondary school report including the transcript and counselor letter, then the letters of recommendation, and finally any supplemental information a studend may have sent.
One thing that this means is that the essay really is important and can potentially create the first impression a student makes on an admissions officer and therefore significantly impacts the student's chances for getting in. It also means that the first impression made comes directly from you.
If a college application does not include an essay then the order would proceed with the secondary school report and recommendation letters – emphasis on GPA and test scores.