I cannot say this as a blanket statement, but from my own personal experience:
Yes, they do accept students with some amount of research in their backgrounds, but they do indeed tend to recruit and place students that have had no research experience.
I was one of those students who had zero research experience when I applied and I got into the two programs I applied to while I was an undergrad at UCSD (Amgen and Scripps Research Institute - Immunology).
My friend, who was accepted at the Amgen, but not Scripps program, did have I think at the time 1.5 years of lab experience, but nothing really substantial. I mean...think about it...most of the type of people they are trying to recruit for these programs are around sophomores going into their junior year, and what not. When you submit your application, you'll only have completed 1 year in college, so even if you did have some lab experience, it won't be publication worthy (unless if you're a genius, in which case you wouldn't really need to be doing this cause you're already in a lab that loves you.)
I had another high school buddy, who went to Cal (UC Berkeley) who applied to the Scripps Research Institute Program, and got in. She had more intensive lab experience than the friend I mentioned above (working closely with a post-doc on stuff, responsible for a small project, no pubs).
So, it's up to you how you portray yourself and as a good fit for the program.
Kinda like med school....
