Unless you are IN a nursing program with the intention of getting a degree in nursing, you wouldn’t be able to take a nursing course anyway - only people who’ve been accepted into the BSN (or ADN) degree program can take the clinical classes. If you are completing a nursing program, then yes, that’s some degree of clinical experience I guess.
The point of clinical experience is to show that you don’t have some unrealistic notion of what you’re getting into. A shadowing experience could blossom into a regular gig that would give you that kind of exposure. If your personal statement demonstrated that as a nursing student or a nurse, you were able to appreciate the weirdness of the U.S. health system and the role of the doctor in it, then that could work.
Volunteer work is NOT the same thing as clinical experience, as efex has already indicated. While it CAN be clinically oriented, in my view its real importance is in showing that you’ve got things you care enough about that you give your time to them. Med schools read 30,000 applications every year that contain some variation on the sentence, “I want to be a doctor so that I can help people.” It is easier to take this statement at face value if your resume indicates that you have, in fact, helped people already.
Hope that helps.