I haven't heard of any allopathic school that offers admissions without an interview. It's unlikely that there's a rule against doing so, but it seems to me that an interview is a necessary component of your file. It's not only how the school finds out about you on a personal level, but a chance for you to evaluate the school as well.
Schools interview somewhere between 2 to 5 times as many people as they're going to offer acceptances to.