It is best to start this answer with a brief description of Transcendentalism. Transcendentalism started in America in the 1830s. It was a response to what was seen as corruption in the church and politics. Transcendentalism believed in the inherent goodness of people and nature. What corrupts these things are institutions. In addition, transcendentalism believes that when a person is self-reliant, he or she is at his or her best for himself or herself and society. This creates for a good society. The most famous persons in this movement were Emerson and Thoreau.
When it comes to Facebook, we can make some interesting connections.
First, Facebook creates false community. The community is virtual. I am sure that the community that people like Emerson envisioned was not virtual. In this sense, we can say that Facebook does not fit well with Transcendentalism, since it only gives the appearance of community.
Second, Facebook does allow people to express themselves apart from institutions. This is very much in keeping with Transcendentalism.
Third, when it comes to the idea of self-reliance, I would say that Facebook does fit well, as it give a forum to people to express their own opinions, rather than listen to others. There is one irony though - there are so many opinions that a person's opinion barely gets noticed.