Attempting to get published while applying? Forget it. If you haven't already been on a team for a few months there's no way you'll be able to bust out enough work part time to get included on a manuscript before many of your decisions are already made, if not all the decisions of whether or not you'll get an interview. Remember that even after the manuscript is submitted it may get sent back for revisions, will stick around a while in review, and may even require you to run some additional experiments.
This isn't to say that it wouldn't be beneficial. It shows that you're still engaging in scholarly activity (which isn't necessary for your gap years by the way) and research always looks nice to the schools that value that. However, I think you would be better served just seeking out full-time work (I know it's hard) and saving up.
Yes, a volunteer position can lead to full-time work if you're showing that you're productive and the PI has the grant money and lab space for you. At the very least you'll learn some skills that might allow you to get a part-time or full-time (both paid) position in another lab if not the same one since they will know that you don't need to be "trained" in any of the techniques.
I think it would be entirely appropriate to ask if there's the potential for paid work. If he says no, it's no big deal. You'll be hard pressed to find a lab that will turn down a year's worth of free labor so he'd still probably let you volunteer. The question is, are you firmly set on only doing work that will translate to paid work? Be wary of PI's that say "yes" to that question but never tell you that the only situation where that would occur is if you already worked for them for a year. It's possible but much more delicate to also inquire if you might get published but, again, that really shouldn't be that big of a concern for you since it's unlikely you'll be published in time for it to help your application.
At the end of the day, volunteer researching will keep any adcoms from having beef with your gap year activities and will teach you some marketable skills that can be used in the future (if you ever continue research in medical school). However, there's plenty of other activities (like working) that would look just as good as researching for gap year activities. Remember that since you're going to be applying, what you do really won't matter that much unless you're doing nothing or literally raising babies from the dead.
