Hi Kasey,
I believe it's controlled on the users individual notification settings, under miscellaneous information. If the user has 'Someone shares an object with me' notifications turned on, they will get a notification when someone shares a document with them.
One point of caution however, this setting applies to all objects (tasks, projects, reports etc.). Turning it off will stop all share notifications from going to the user.
Best Regards,
Rich.