Will a publication help your application to medical school, particularly Stanford? I would have to say yes. It can even shade the letter of recs, because the PI gets to say that you contributed to work that has been published. You can decide if the lack of an advantage is a weakness or just baseline. Is it essential for getting into Stanford? Of course not. However, I think about 1/3-1/2 of starting med students at Stanford have been published already. Someone else reading this can correct me if they have better data, but that is about what I remember hearing. Keep in mind though that this is scaled by where you are in your life path. I think four people who started in 2013 who already had their PhDs, and other people had various bits other graduate training. I don't know what the makeup of the class starting in fall of 2014 is yet, as I've only met a fraction of them.
I'm sure you've heard/read somewhere that a major thing is to differentiate your application. People differentiate themselves many ways, including things like lots of community service, overcoming adversity, high level of non-academic achievement (sports, art, business, technology) etc. However, I would have to say that overall, unlike undergrad, Stanford Med likes "pointy" students rather than "well-rounded" ones. And if one of your main pointy areas is in research, then you probably have to be as pointy as possible, which means really excelling, and the way excellence in academic type research is (perhaps unfortunately) measured is publications. Overall though Stanford definitely tries to have everyone be their own "special snowflake" as much as possible, so they honestly try to holistically select good candidates to interview based on a wide range of features.
Overall, I don't have good data on it, but I have seen a handful of people who applied, didn't really get much traction, and then after a few years doing research and a publication, got lots of interviews that led to acceptances.
I don't want to discourage anyone. However, in review, at a top ranked research school, as far as I can tell, a paper does add to your application, and a lot of other people applying will have 1+ publications. That being said, your application is what it is. Just like everything in life, including medicine, you do the best with what you currently have available, and that includes your CV.
Also, as your going along and start stressing about your application and whether you are going to get an interview or an acceptance, and then get caught into thinking that it is of incredible importance to go to Stanford, remember that most of residents/fellows in the various programs at Stanford didn't go to Stanford for med school. Obviously, many Stanford students often stay local, but there are still way more students from outside, and there are more residents and fellows than students anyway, so more slots. Then, beyond that, there are tons of faculty who didn't go to Stanford who obviously spend way more than 4-5 years here. There are plenty of opportunities for your medical career to intersect with Stanford. Good luck! I always say it is a marathon, not a sprint, as long as you are working toward your goals, you're going in the right direction.
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