"Noam Chomsky is an ardent believer in democracy (...) Chomsky is evasive or worse about discussing his own voting. He dodged a question about whether he votes for the Democratic Party. He suggests that anarchists should vote in "swing states." (...) Chomsky lives in Massachusetts, which always votes democratic, so he should never vote in national elections. But he does. (...) Ultimately, Chomsky did vote in 2004--not for Kerry, as he was advising other people to do, but for Ralph Nader, the Green Party candidate, who was even more authoritarian than the majority party candidates. Nadar advocates making voting compulsory."
- "Chomsky on the Nod," Bob Black, Defacing the Currency.
http://littleblackcart.com/Defacing-The-Currency.html
Black goes on (and on), but I won't tire out my hands any more, because the answer is yes Chomsky believes in the democratic process and voting.