I like Chomsky's books and documentaries, but I've never connected him with the Chinaski character.
Chomsky is a Libertarian Socialist (or anarchist, if you like), but I don't think the Chinaski character has a political persuasion as such. Chinaski seems rather a-political to me. Sure, he criticizes the establishment (as in Barfly - "Why do everybody have to be somebody?"), and so does Chomsky, but Chinaski does it from his own personal viewpoint and situation, while Chomsky, being the scholar he is, does it in a systematic way.
I don't think there's a connection just because both of them criticizes society, because people do that all the time from entirely different viewpoints. I might criticize society too, but that does'nt (necessarily) mean there's any similarities between the Chinaski character and me, or Chomsky and me.