nope - no value in a twitter link whatsoever except the one link ur allowed to have in ur twitter profile. that one has a little juice but individual tweets do not.
Twitter will drive traffic only if you have huge number of followers for your profile. Otherwise it is just a scrap and no use. Hence you may need to increase your followers by adding them as your friends. But the links may not have any impact on SE rankings.
if you want to jump start your twitter you need to automate some processes and great a viral incentive to get ppl to retweet your stuff and follow you. add value but keep it very specific to your niche. extremely niche focused is the best way to go.
Twitter links (aka Statuses) are basically nofollow links. This means that they do not contribute to your site's pagerank. But they are do crawled by Google from time to time, so you still have your twitter links available for google search. This is a good way to promote your articles especially when you're still working on your pagerank. But there's also one thing that makes Twitter unique. There are other crawlers and bots (from other sites) that gets your twitterfeed and they post it automatically in their sites. Some of these sites are dofollow so in an indirect manner, twitter can still help you acquire a good pagerank.
It does help get indexed, and there are rumors that it can help some with rankings. It's definitely important, as it's going to be how "quality content" is determined.
In that case I would say my twitter page is having PR5 pagerank, so my site which link, I have placed on that page should atleast get a PR3 No social networking sites like twitter, facebook and so on do not have any importance for their user profile pages.