I agree w/above, I don't think its necessary or beneficial to say you've been accepted elsewhere.
But, I would definitely send the LoI. I used a LoI to express sincere, individualized compliments and a couple relevant application updates to what I believe is my 1st choice school. I don't let the fact that I sent a LoI get my hopes up, but I imagine any edge you can get--especially just writing a little letter--is worth it. After my interview it gave me the chance to play up things that I felt with hindsight weren't touched on in my interview. It's also no secret that many accepted students are accepted to more than one school, and when school A accepts these people many of them go to B, resulting in pulling from waitlists, etc. To me, using an LoI to break a close tie seems efficient and would make the school seem more competitive because they could accept fewer students.
And at the end of the day, even if the adcom who gets your letter isn't receptive to it, good on you for being assertive, professional, and respectful to his school by humbling yourself and being so explicit about what you want.
