There's another aspect of SEO that relates to Twitter. And that's how your Twitter account itself appears in search engine results. I have a good profile to gauge this effect because I share my name with that of a famous Aussie cricketer. So quite a few people search for it every month. And one of my Twitter accounts has the name Matthew Hayden in the handle (although the title that appears is Matt Hayden).
What I've noticed is that if I've been very active with that Twitter account, it will appear higher in Google results for searches for the name "Matt Hayden". (Searches for "Matthew Hayden" are completely dominated by the cricketer.)
Right now, for instance, my profile appears about halfway down the first page. I assume that's due to the fact that I've been very active for several weeks. But before that I was on page two.
This has ramifications for anyone wanting to use Twitter to promote themselves or a product or service. If you use keywords that aren't completely saturated in your Twitter username and tweet up a storm for a while then you may well end up on page one of Google for searches for them.
If you include a website in your profile then a certain proportion of visitors arriving at it will click through to it. It won't be a large number, but it will certainly accumulate to a reasonable amount over time. And it will be targeted traffic too. So, this is definitely something to aim for if you like using Twitter.