One way it could work: you could "follow" a publishing company and then direct message them in regards to a particular post they've made about an upcoming series of books/book from a particular author/what-have-you that you'd be interested in working on.
Lots of companies who use Twitter will only make a half a dozen posts a week. It's not that hard to keep up with. You don't have to tweet at all, you can just follow a bunch of publishers, authors, fellow illustrators. It's a good way to catch up on the buzz of your industry.
That's more of a long shot, though. However, I think anyone looking for work should get going with Facebook or LinkedIn, if they're not already. Because people can and do network on those.