I'll add just a bit, from my own experience. I was an admissions officer at a very selective university for almost eight years. I read thousands of applications and essay responses. I've also worked as a college counselor in three high schools.
Submitting a poem as an essay response is a risk. I wouldn't categorically say it can never work. However, it's a risk because of its genre: a poem evokes emotion. A poem leads the reader to linger. In doing so, it may, or may not, answer the question being asked. The emotions that often inspire someone to create a poem don't always fit the tone of what's asked by the application question. If the question is: "Why do you want to attend our college?", or "Tell us about a person who has been influential in your life?", it's the rare applicant who will be inspired to answer such a question in the form of a poem, because the replies need to contain some specific information, and they need to clearly convey what you, the applicant, want from your education or how you've learned to be a better person from your mentor or hero.
The genre of poetry, in other words, isn't easily suited to the intent of the application question.
If, however, a student thinks in images and sensory language, and feels he can best express his answers via a poem, it's crucial to remember the reader.
As a former English teacher, I saw that most students reacted with some nervousness to poems in the curriculum. Having studied plenty of poetry myself, I can say that one needs practice in reading them in order to feel comfortable with their ambiguity.
What I'm saying is that, in my experience, admission officers--like all of us-- may fall into several camps: those who enjoy a poem but don't have the time to linger over it; those who don't particularly like poetry or are a bit nervous that they won't "get" it, or--perhaps most concerning for the applicant-- those who may be poetry lovers, or even poets, themselves. If that's the case, they can't help thinking about how "good" an applicant's poem is.
So if you are absolutely drawn to answer an application question with a poem, it is imperative that you solicit the advice and feedback of someone who knows poetry--preferably a college counselor or a teacher who's worked in admission or has some pretty deep experience with college essays--before you submit a poem. Don't submit a poem without having someone who knows poetry, and knows college admission, read it. And find out as much as you can (which I hope you would do anyway) about the college's emphasis and atmosphere and what it values.
I'm glad you feel an impulse to write poetry! And I'm glad you asked the question of this forum. Best wishes with your applications.