Yes, it can. Here is a quote from one college admissions counselor in College Essays that Made a Difference:

There are essays that are compelling, that make a difference. A great essay can carry the student. A poor essay might do the opposite. – John Latting, Director of Admissions at Johns Hopkins University

In general, small schools weigh the importance of the essay more heavily than a larger school. The U.S. News and World Report Ultimate College Guide is the only college guide that lists how important the essay is in a college’s admission decision: very important, important, considered, not considered. For example, here is a listing of essay importance for Michigan colleges.

Here is another article on the topic:  How Much Do College Admissions Essays Matter?

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