I doubt that small-town libraries will get rid of all books. Libraries do have collections of local history which are unlikely to be part of a digital archive. (Eg, phone books from the 1950s, local high school yearbooks, photo collections and films about the annual downtown parade, publications from the local genealogical society, etc.)
But if in 100 years small-town libraries have mostly switched to digital collections, then yes, it's possible for the knowledge to disappear even if the infrastructure remains.
I don't think it's likely, but it's not completely inconsistent.
I can envision a future where libraries have few books. Here's one at a school in Florida - http://www.reuters.com/article/2014/08/25/us-usa-florida-lib... . Here's a broader commentary about libraries which don't have physical collections, including a public library in San Antonio - http://www.mnn.com/lifestyle/arts-culture/stories/is-a-libra... .
I doubt that small-town libraries will get rid of all books. Libraries do have collections of local history which are unlikely to be part of a digital archive. (Eg, phone books from the 1950s, local high school yearbooks, photo collections and films about the annual downtown parade, publications from the local genealogical society, etc.)
But if in 100 years small-town libraries have mostly switched to digital collections, then yes, it's possible for the knowledge to disappear even if the infrastructure remains.
I don't think it's likely, but it's not completely inconsistent.