Is it possible to participate as a research assistant as a nondegree student?
This wouldn't work for me as an employer of research assistants. Undergraduates and random people off the street rarely have technical sophistication to be able to participate in my research projects. I'm pretty sure that in most cases I'm beholden to my NSF grant terms to pay a PhD, a postdoc, or a student to do the work, since this is what we said we'd do in the grant application budget. The people may be more or less interchangeable to the granting agencies as long as the work gets done, but I believe there's more to it than that. 

I don't think a non-degree-seeking person can be a/an (graduate or undergraduate) research assistant under my university's HR rules either since they must be currently enrolled as an undergrad or graduate student to have either of those titles. Also, I'm basically not allowed to have an unpaid research assistant nor am I interested in such a person. First, it's probably illegal in the US, and second, it's a bit off-puting to me that you would come, do some research, and then leave once you've gotten the publication that you think will get you into grad school. I prefer to have a deeper, longer relationship with my research collaborators than what it takes to get one good publication out the door.