Eh, depends on the lab. Some PIs go the extra mile for undergrad students. Most pawn them off to a postdoc or grad student.
It can still be a valuable experience even if you are not working directly under a PI. It will depend on the project, your role, your level of skill, and how much the PI and grad student care about this project. I would say a good measure would be how "hungry" the grad student or post doc is. Getting pawned off doesn't have to be a bad thing. However, the end goal should be to work on your own independent project within the lab and be treated like a young grad student might be treated - provided you actually care about research.
P.S haven't seen you in a while Reckoner.
P.P.S I appreciate the new Confederacy of Dunces reference, or maybe I never noticed it before
If the goal is to get published well...that really depends on the field, the lab, the project, your skill set, your level of involvement and will, and a ton of luck. I'm on a project right now that will either result in a publication or just more work in three months depending on the results of a few experiments and calculations. Sure there's a hypothesis but if science was certain then this job would be boring and non-existent.
My advice: If you have tried out research and enjoy it then continue, if not just quit. I think everyone should try research but a lot of it is VERY TEDIOUS, boring, arbitrary, and incredibly confusing for very amateur scientists, as most premeds are, myself included. If your goal is just to get published to put it on your resume then it really isn't worth it. Your time is best spent somewhere else. Research isn't even listed by the AAMC in their report about what adcoms think is most important for acceptance into medical school. Research is key at only a few institutions in this country and if research isn't for you then these schools are most likely not for you (not necessarily, but you get the point). Thinking like a scientist, understanding the process, developing curiously and a capacity for original thought should be your primary goals as an undergraduate researcher. Secondary goals, provided you wish to continue with research as a career, is to familiarize yourself with the politics of academia, gain enough lab skills so that you can work in a variety of labs in the future and can be an asset in said labs. Publishing is the icing on the cake. "Publish or die" applies only to PhD students.