In my opion, twitter can improve your writing skills. When writing, you will think over how to write, how to use good vocabulary, how to use phrase, how to describe and express your meaning in one or two sentences and all of these are helpful for your improving your writing. However, I think writing in a blog and taking suggestion from your friends can help you make a progress.
Probably, twitter is way too multi-purpose. If you're following the right group of article writers, you'll probably gain something useful from their tweets, like articles on useful tips for article writing.. etc. (I'm not an article writer of course)
With twitter being a microblogging site, it won't improve you vastly in my honest opinion. However, it can improve relevance of your writing, and getting used to not wasting space with excessive wording
Not sure if twitter will make a person a better writer, but will force a writer to think more creatively in the sense that they need to convey a message in 140 characters. Another area that I reckon makes a person a better writer is forum roleplaying. It forces a person to think about your characters and describe the surroundings better etc. If you join a forum where they rate your work and have people help you, then you end up being a damn good writer. Some writers I know that are younger than me write and describe better than Stephen King himself. Yet they are not concerned with earning a living as a writer- to these people it is only a hobby. Shows you what you find if you look really hard.