git works fine with LaTeX (almost any text-based source, in fact), so why not? I'm using git for almost everything I write (mostly not shared, some pushed to a git server for backup, others locally shared), and also to work with my students on their theses (mostly reading what they write, sometimes sending a git patch for their consideration). On a project we had a set of BibTeX files with the references for our papers and general references used in our writings, all shared though git. We set up a private git server for this.
You can pay for having private repositories on github, AFAIU. Or you can use their free service to share stuff under an open license with the world. Just make sure you really want to give up your rights in the second case. Perhaps think about what the Creative Commons licenses would mean for your work, check what github asks from you.
LaTeXdocument, and the structure (self-written packages etc?) Perhaps, it is better to provide thepdf- version of the document rather, unless there is cooperative writting of a group on the same document. – Feb 25 '14 at 18:44