Regarding the volunteering -- I think it would really depend on the library system. The large urban system where I work takes on volunteers for pretty specific, mostly low-level tasks. I've never heard of the possibility that someone could be taken on as a volunteer doing the sorts of activities that would be relevant to a budding professional. (Though that might work in the area of children programming.) Of course, if you want to do shelf-reading or tech assistance (e.g. helping people sign up for the public computers), I'm sure any public library system would welcome you.

On the other hand, right after I got my MLIS, I contacted a suburban public library where I'd worked as a clerk and asked if I could do volunteer work and be "mentored." They were enthusiastic, and I spent a few weeks before I actually found a job helping with a weeding project and revising some topical Web guides. So that was certainly beneficial to all parties, but the set-up was unlike my current centralized/bureaucratic system, and of course I did have a history with that library.

Good luck whatever you decide to try!