it depends on what region of the country you're in. In the midwest or south, there tend to be more married students than in the big east/west coast cities, I'd assume. However, in my class, only a handful of students are married, and another handful in 'serious' relationships (as in, very likely they will marry the person eventually). Maybe 10-20% of the class total. Lots of people are dating, mostly non-med students, but I don't really look at it as 'serious' until there is a ring on the finger (and even then...).
So yeah, you shouldn't have any problems making friends if you're single. My class is very social and have quite a few social events aka parties. I am not very social but have a couple of friends who are either single or 'dating' (and I'm friendly with the married students) who don't do the party scene. However, I emphatically subscribe to the rule of not dating fellow medical students, and therefore where I live has 0 options on that front. So if you want a healthy dating life (not that you really have time for it), you should try to be in a major city. And not every medical school is in or near an undergrad campus (many of the midwest ones, mine included, are in satellite campuses hours from the nearest frat/sorority house)