Twitter is a great way to build back links to my sites, but because tweets are not indexed by Google they don't really drive as much traffic to my site as maybe we would all like to think. You should not use Twitter as a main SEO tool. I have had twitter pages show up on the 1^st page of Google, So it would make sense to add it to your overall SEO practices

If you have more than a few accounts on twitter “which is a wise thing to do” you can leverage them to build awareness of your brand, and in doing that you will aquire some back links.

There are still many of people who don’t use the third party apps like TweetDeck and others that will click through from your twitter, Plus with more social media platforms letting you connect to their website through your twitter account, “like FriendFeed” it can all add up to more back links.