Yes and No
A competitive program that receives a large number of applications, such as a doctoral program in Clinical Psychology, may receive up to 500 applications. Admissions committees for competitive graduate programs break the review process into several steps.
First Step: Screening
Does the applicant meet the minimum requirements? Standardized test scores? GPA? Relevant experience? Is the application complete, including admissions essays and recommendation letters? The purpose of this initial review is to ruthlessly weed out applicants.
Second Step: First Pass
Graduate programs vary, but many competitive programs send batches of applications to faculty for an initial review. Each faculty member may review a set of applications and identify those with promise.
Third Step: Batch Review
In the next step batches of applications are sent to 2-3 faculty. Now applications are evaluated with regard to motivation, experience, documentation (essays, letters), and overall promise. Depending on the size of the program and applicant pool the resulting set of applicants is reviewed by a larger set of faculty, or interviewed, or accepted (some programs do not conduct interviews).
Fourth Step: Interview
Interviews may be conducted by phone or in-person. Applicants are evaluated with regard to their academic promise, thinking and problem solving skills, and social competence. Both faculty and graduate students evaluate applicants.
Final Step: Post Interview and Decision
Faculty meet, gather evaluations, and make admissions decisions.
The above process varies depending on the size of the program and number of applicants. What's the take-away message? Make sure that your application is complete. If you're missing a recommendation letter, essay, or transcript, your application will not make it through the initial screening.