Almost certainly and almost always, the answer is “yes!” Classifying exactly how and precisely how much is a more challenging question, but search engines like Google and Bing do access some forms of data from Twitter, Facebook, LinkedIn and Google’s new Google+ (to be honest, Google doesn’t use too much directly from Facebook and Bing probably isn’t using much from Google+, but you get the idea).
Sharing links on Twitter may have a direct positive impact, and an indirect one, too.
But, even if/when the search engines aren’t directly taking signals from Twitter, Facebook, LinkedIn, Google+, etc. these networks are helping to spread the word about your site and your content. Using them to promote your posts in organic, natural, useful ways is a great thing, and you should almost certainly invest some effort trying out these networks and discovering whether your blog is a fit. Twitter in particular has been a huge driver of traffic for Geraldine’s blog, so I suspect there’s value there for many other travel blogs. Facebook has been good, too. LinkedIn, less so, but this is likely because it’s geared toward a business + career focused audience. If your site caters to business travelers, you could well have a great match there.