Should councillors Twitter?

A website has been created which lists councillors who Twitter. I have registered to Twitter, in order to read the Twittering of others, but I haven't actually done any Twittering myself yet. This is something I feel a bit guilty about as I have had several emails saying "so and so is now following you on Twitter" and I worry I have been letting down my fans.

Twitter is a micro blogging. People write very short entries on what they are doing or thinking or about to do at that moment. I suppose a bit like people who write on Facebook: "I am now going to have a cup of tea." Or "I am now going to have a bath." But in Twitter anyone who wants to can read such updates - rather than just those who are your "friends."

Have any councillors found Twittering productive so far?