If you have an absolute favorite school, I see no reason why you shouldn't send them a letter of intent. Worst case scenario, they ignore it and you know that you did everything you could.
In some cases (like mine) I really do believe it helps. I sent my school a letter of intent shortly after being waitlisted, and although I didn't get an immediate acceptance out of it, the program director called me the next week, and called me several times over the following weeks just to let me know where I stood with the program (when accepted students declined offers, when committees were meeting, etc). I don't think that would have happened for me without the letter, and those phone calls really helped me deal with the whole waiting period (and they reinforced how much I liked the program and the people there).
Yes, this is an anecdote. Yes, anecdotal evidence is patchy, blah, blah, blah. But, this particular case is close to my heart, so I'm cool with it.