I was accepted to AZCOM without a letter from a DO, but I did have a great LOR from an MD whom I have known for many years.
That said, I would recommend shadowing a DO for a day at the very least. I shadowed a family practice DO in a town 2 1/2 hrs from where I live (the only one that would return my calls in a 3 hr radius from my home town.) From this one day, I got to see OMM in practice, list that experience on my apps, and was able to better describe osteopathic medicine (a common interview topic) from that exposure. This way, schools could see that I knew what osteopathic medicine was about, even though I didn't get a DO LOR (I personally had a problem asking a person who had just met me to write a letter, even if he did have the initials DO behind his name.)
Hope that helps, and good luck with your applications!