I wrote a letter to QF after my interview last year (3rd stage). It wasn't a 'please re-think' letter, but more of a 'thank-you for this opportunity' letter. I wasn't expecting a reply and I didn't get one.
A reply would have been nice but I'm guessing that I am not the only one who wrote to them, and I can only imagine how time consuming answering all these letters would be.
But I agree with ditzy-boy, it wouldn't hurt one little bit to give it a go!!!
--Just make sure you write it in a positive tone.
love SMILE