They would count toward clinical experience, for which many premeds volunteer at hospitals. However they don't count as "volunteer service" in the charitable sense -- so if the question is whether the schools that care about charitable/civic/church non health stuff (and a handful of schools ask re this) will count it as such then the answer is no.
No, you must voluntarily sign up to do clinical rotations outside of your normal curriculum if you want to fill in the volunteer box on an application.
Since you already have lots of clinical experience through nursing school, you may want to try volunteering in something that isn't medically related (e.g., Habitat for Humanity, teaching English as a Second Language, etc...)