I would never ever let my child sleep in vomit! How cruel. If my child's pediatrician suggested such a thing, I'd find a new pediatrician ASAP.
I don't believe in CIO either. I know I would hate it if I was scared or upset and no one came to comfort me. I also wouldn't recommend staying with a child until they fall asleep- because I did that with my 1st child and he still couldn't fall asleep on his own when he was nearly 4. I wasn't sure WHAT to do. Then I saw an episode of The Supernanny where she was showing parents with the same problem what to do.
I started sitting in the room, near his bed, where he could see me. I had myself positioned so I was not facing him, but he could see the side of my face. I would sit there, but no eye contact, no communication. Each night I would sit a little farther away from the bed until I was in the hall but where he could see me. Then I was in the hall, but just out of sight (but he knew I was there). After that, I could be in my room reading a book or magazine until he fell asleep. Never got to the point where I could be downstairs. He was too afraid to be alone upstairs at night, but that was ok with me because he was at least falling asleep on his own- and I would just wait to go downstairs after he fell asleep. The whole thing took about a week, but was worth it.
Hope this helps, it helped me a lot. Good luck :)