it doesn't mean it's "improbable" i don't know what rush's policy is, but i am sure you have an excellent shot at an interview, otherwise you would have been rejected.
i just think (and if anyone knows better, please correct me) that it would be difficult for an adcomm to take a letter of intent seriously if you haven't gone to an interview yet. letters of intent are best reserved for later on in the process, in case you are put on a wait list after you've interviewed. you've seen the school, and they've seen you, so when you gush about them in your letter, and tell them you are completely devoted to them above any other school, it sounds more sincere.
i would strongly advise first talking to your school's premed committee or premed advisor to see if they can help you out now. med schools will love to interview people who are very interested in them, and having someone with authority to pass along that message indicates to schools that you really are worthwhile, and aren't just sending out the same letter of intent to every place. of course, if you can't get your school to help you, go ahead and send the letter. it can't hurt.
