This is a wonderful idea, and a lesson that so many students need to learn. This lesson is grounded in a real-world and authentic need, which serves to motivate students and keep them engaged. Using a popular video will also serve to spark their interest.
Do students have a choice on which site they use to explore privacy settings? How would you account for students who do not have a social networking account of any kind (I imagine this issue would come up less than infrequently, but one never knows). What about school firewalls that prevent accessing these sites?
I would recommend some kind of blogging/sharing/collaborative experience to accompany this activity where students justify why they made the changes that they made to their privacy settings. Facebook has so many settings and options; there are sure to be a wide variety of settings chosen by students. By supporting and defending their choices, students would demonstrate understanding of reasons behind changing privacy settings and help their peers understand different choices as well.