I heard back about a month later, a few days after the decision deadline. I'd paid the deposit for another school by then and had to request a release.
I believe 3-5 students got in from the waitlist in my year, but it does vary from year to year.
For the statement, be enthusiastic and specific - show that you've done your homework and know why this program is the best fit for you, and what you'll add to it. Then send it in and try to forget about it (not easy, but better for your happiness these next few weeks). Good luck!