This is a feature that some people will like, and other people will hate. I have integrated Twitter onto one of my game websites as a replacement for the announcements system. The users of my website love it, as they can either see the announcements when they login, or they can see them as they are made on their Twitter account. I have also found that Twitter integration has brought new people to my game, it is a great promotional tool.
It could also be a good idea to give users the choice of using the Twitter module on their profiles. This can easily be configured using the Twitter API code. You would just need to add a field where they can enter in their Twitter username, create the database table, and insert the code into the API.
I will have a muck around with the Twitter API and will post any progress.
