Alina,
There are definitely people in the program who had no research experience before. The original purpose of the program was to try to get more MD's interested in pursuing research, because they have a different perspective on problems than PhD's. It is true that having some research experience is probably beneficial, but if you seem like you are genuinely interested in research, and it is an option you want to consider in your career, you will have a good shot, and should try to apply.
Is the program worth it? Well, you have the freedom to choose any lab to work in, so you can in a large degree determine what you get out of the program. If you are interested in getting a first author publication, you can pick a lab with a good publication record (you can also find out which labs students have choosen in the past, and do a pubmed search to see what publications they got out of the labs - there are a few labs where more than one student has gotten a first author Science paper!). You will have an advisor when you start the program, and they can help you find a lab which suits your goals.
You can apply after either your second or third year. I applied after my second year, but now I'm kind of wishing I had gone after my third year, for several reasons 1) I haven't decided which field I want to go into, so choosing a lab was hard. 2) I'm thinking it's going to be hard to go back and do a whole year of rotations - I'd rather be going back with only 4th year to worry about
Still though, I expect to get a publication out of the work I'm doing (although it probably won't be in a super high-impact journal). The experience has been great so far, I've met a lot of famous researchers, and I'm having a blast living here, so I definitely think its worth it. Also, ask some professors at your school what they think of the program. I have heard different things, but a lot of people here seem to be convinced that people think pretty highly of students who have done the program...
One more thing: every year, 4-6 students in the program receive a scholarship which pays for the rest of their medical school education plus a stipend to live on. Considering that there are only about 42 people in the program/year, everyone has a good shot.