Do schools/departments ever evaluate their own admissions process?
This practice is not frequent, and it is rarely systematic and rigorous.  However, from a decision-making perspective, this has been given attention by Robyn Dawes, who was a very well-known psychologist at Carnegia Mellon.  Here is one of his papers on the topic, which has been cited about 500 times (per Google Scholar). Some recent evaluations have been published, but relative to the total number of admissions committees that exist across all graduate schools, I can confidently say it is not many. 

Dawes, R. M. (1971). A case study of graduate admissions: Application of three principles of human decision making. American Psychologist, 26(2), 180.