Do you mean non-medical volunteering or just non-medical "stuff" in general?
I think as long as you are volunteering and putting in the time, then schools will recognize that. BUT, if medicine related stuff is all you do...then they might ask "What do you like to do BESIDES research/clinical/medical volunteer?"
You don't have to like "chess" or "debate" to have extra-curriculars. EC's are the things that make you...well, YOU. One of my most important EC's is my music...playing in bands..practicing...and teaching students. Another is that I like to read books about history and politics. I spent a good amount of time with my little brother, helping him with homework and life in general.
None of these are associated with my university or any "clubs." But I could tell you exactly why each of them is important to me and how they have shaped me as a person.
Just relax and do some cool stuff. Now is the time for it, before medical school and residency. Don't worry about how it looks on an application, adcomms can spot a contrived app so easily. With GPA and MCAT as universal requirements, do you think med schools really care whether you have 200 or 300 hours of clinical volunteering? Whether you are involved in "medical" stuff every waking minute? No, they want to see that you are interested and involved in the world around you, and there are SO many things you can do that fall into this definition.
Adcomm members know that even with all the medical related EC's in the world, no pre-med student is going to really know anything about medicine until med-school. Sure, you may learn a specific set of knowledge for your research, or watch some neat things shadowing. You may even succeed in impressing your friends with your relatively tiny amount of medical knowledge. But the truth is, your medical education does not start until you begin medical school. Therefore, why be all obsessed with medicine right now? You have the rest of your career coming up where you will be required to be obsessed with medicine.
Are adcomms looking for people with a passionate interest in medicine? Yes. But generally, people like this are into other aspects of life too.