Crazy as this is, there's a scholarly study of the Inspectrum fandom "Reifying the Fan: Inspector Spacetime as Fan Practice"*, even though the show does not, of course, exist anywhere except in our imagination.
Then again, I disagree that the essential text for the understanding of Inspector Spacetime is Roland Barthes' essay "The Death of the Author". In the first place, Dan Harmon is still alive, after all, and has returned as Community's showrunner. More important, Harmon dislikes the traditional "one-way transmission" model of television and has openly embraced the Internet as a way to communicate with his audience and as a medium for collaboration, from his voluble Twitter and Tumblr accounts to his pre-YouTube video site Channel 101 and its associated Wikia.
A better candidate for the Inspectrum's bible would be Borges' short story "Tlön, Uqbar, Orbis Tertius", in which a factitious encyclopedia article leads to the discovery of "a secret society of astronomers, biologists, engineers, metaphysicians, poets, chemists, algebraists, moralists, painters, geometers" involved in the documentation of a fictional world that will eventually supplant reality. (Admittedly, the Inspectrum isn't that ambitious.)
For the Internet-based media where the Inspectrum has flourished, there are also some other literary antecedents. TV Tropes's Inspector Spacetime cataloguing project could be the offspring of J. G. Ballard's experimental short story "The Index"; Tumblr's Inspector Spacetime Confessions resembles a digital update of the Surrealist game parallel collage; and here on this Wikia site, we're creating something that might one day rival the Dictionary of the Khazars.
Not bad for something that started as a 30-second pastiche of Doctor Who.
* Full Disclosure: I answered some of the academic's questions about the Inspectrum and received an acknowledgment in the published work.