This probably won't net you much. They know you want to go there, and at some point in the cycle they will know if you haven't been accepted anywhere else.
Thank you!
The only time this is a good idea (usually called a letter of intent) is if you are accepted at a "higher tier" school and are on a waitlist at your first choice. It lets them know you want to attend your #1 over somewhere that historically applicants choose over the school in question. Otherwise you're wasting paper.
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