I know that this can be done, but as it's not something I'm interested in, I don't recall the exact details. I know that some folks are using Dropbox for this purpose.
Perhaps DoctorOoh! might know more? He's a Dropbox user (and mentioning his name gets
both of you extra storage space).
One warning: Google's file-sharing service
may not be usable for this purpose. When you add a book to calibre, it stores the ebook in a folder with the book title and a number (example:
Alice in Wonderland (2801)). Google's file-sharing service uses that
(#) format for it's own internal needs -
and strips it out of calibre's folder names without warning - ruining you calibre library! I believe Google has been notified, but I am not aware if the problem has been resolved. So be careful. And keep an offline back-up of your library as a precaution.
Until someone more knowledge replies, search on the terms: file-sharing, server, cloud. There should be multiple topics available in the calibre forums on how to implement this project.
PS: My comments are for using a server and file-sharing service on/through the internet, so my answer may not answer your specific needs.
Is this of any help:
COPS: Calibre OPDS and HTML PHP Server