Yes. Sometimes. Rarely though.
People will read an article or page word by word if they're really interested in it. However the majority of people will skim the site reading certain words, subtitles, bullet points, smaller paragraphs and images. People believe that skimming will get them to the information they're after a lot more quickly, which may or may not be true depending on the person.
So what does this mean? Basically don't give them large paragraphs, promotional writing or adverts, small talk or pointless and irrelevant filler.
In 2008 on average about 20% of text is actually read on a webpage according to a study by Jakob Nielsen.
So why bother? If we're writing for a specific segment of people then someone will find it useful and read it word-for-word. I guess the question is; does the content make enough of a difference to someone to make them want to read it?