In my experience, MD-PhD admissions committees find it a bit odd if there is no mention of research in the PS. While the PS can be about anything (I've even seen poems composed specifically for it), MD-PhD adcoms expect to see something about research there. The statement is supposed to convey a sense of who you are to the adcom. It seems that whether you write about past experiences or future dreams, if you want to be a physician-scientist then research should be mentioned in the PS. If research is not mentioned, adcoms might wonder about your commitment to research.
Yes, we have offered admission to individuals who did not mention research in the PS, but that does not mean that when we initially read their application we did not wonder if they were really commited to the MD-PhD. This question did crop up, but the rest of the application & letters of recommendation were compelling enough to tip the balance for an interview. So you can get by without mentioning research, but the prudent approach would be to include it.
Research should not dominate the PS. You only need to mention it in the context of what you have done/or hope to do, and how that fits into who you are as a person. A short paragraph, say three or four lines, is sufficient.