This is a great question. There are many ways in which to look at the connection between transcendentalism and Facebook. Let me give you some points.
First, transcendentalism espouses two main views. First, people are inherently good and organizations and structures corrupt people. Second, people and society are at their/its best when there is self-reliance. In light of these two points it can be argued that Facebook does and does not fit in.
On the one hand, it fits nicely with transcendentalism, because it gives a public forum for the exchange of ideas without constraints. There is freedom from institutions. In other words, people have their own voices. Some revolutions have been abetted by social media. This is an important point to keep in mind.
On the other hand, Facebook also shows the intolerance and evil in people's hearts. This does not show the inherent goodness of people. Recently there has been news about bullying on Facebook and social media. This would not fit in well.
In the end, it is safe to say that opinions will be polarized and the outcome will therefore be interesting.