Yup. It would. My kid’s first attempt at an essay was about how the local music school arbitrarily rejected him (because of his age), and how he showed them by winning an international competition that year. No matter how he put it, it came off as obnoxious and braggadocius. And since that achievement was listed elsewhere in his application, it told them nothing they wouldn’t already know.
The college is going to see your SAT score, and they know how that ranks you against others. Frankly, stating that you prepared at all for the SAT won’t help you - it will make them think that your high score is due to professional tutoring/prep. They will see your score - don’t waste your essay drawing attention to it. Better that they should think that you walked in cold, with no prep, and got that score.
From what I understand, you don’t want to use your essay to TELL them something about yourself (especially about your grades and SAT, which they can see for themselves); you want to use it to SHOW them something about yourself. You might find it useful to google New York Times college essays about money. These are essays that the NYT thought were excellent, and that all have something to do with money (from both rich and poor kids). It’s a very broad qualification. Some of these essays are very powerful. None of them say, “I did this, and then I did that, and boy did I ever show them, when I did this!” The kids talk mostly about their lives, in a way that allows the college to infer a lot about who the applicant is, what the environment they come from is like, and how they were shaped by it, how they feel about it, what their goals are.
There are also college prep-class websites that will give a lot of free information about how to write your essay. In fact, I believe there is some good free advice here on college confidential about essay-writing. Try reading some of these essays, and then think about what is important to you, what matters about you, what you would like the colleges to know about where you come from, where you want to go, and why. It doesn’t have to be wide-ranging. One of those NYT essays is about the kitchen table in an Appalachian home, and the changing faces of who sat around it, as the applicant grew up. Boy was it moving, and it told a lot about who the applicant was, what she had come from, without just stating the bare facts.