Do I need an active internet connection to run CS6

Though Adobe does not officially support remote disk File access .You can use it open and save files on a remote disk via network sharing.  Saving may be done as a background task I do not know if opening is. And Actions and Scripts use shared network files.    If  some CS6 process was processing a network file I think  that process may Hang or may see and error.   So I think Photoshop  could Hang/Freeze if it was using network files.  I do not think an error reflected to a Photoshop process would crash Photoshop.

Script can also use HTML Protocol to transfer files from web servers. I would hope that a disconnect would be reflected as an error and not cause a hang.