It would be as incorrect to assume the internet is important for all books as to assume it is irrelevant to all books.
I'll think that one over and get back to you once I've got 50 posts and graduate from New Fish to Thread Starter.
In the meantime, to get back to the OP's question: I definitely think that blogging chapters of a NF book can be helpful in attracting the attention of readers and publishers. If the book is actually a good read or somehow useful it will probably find an audience beyond the limits of the blog format.
I wouldn't blog an entire book, mainly because it would be a waste of bandwidth. Have you ever tried to read an entire book on a computer screen? Reach for the aspirin! (A downloadable ebook is another matter, so I won't digress further into that topic.)
Assuming you do publish your entire masterpiece on a blog, only a few hardy souls can be expected to plow all the way through it. If they think the book is great, however, you've just gained your most effective marketing tool: "the talker".
Or, to paraphrase the Furry Freak Brothers, "Word-of-mouth will get your book through times of no marketing budget, better than marketing will get you through times without word-of-mouth".
From an author's standpoint, word-of-mouth and building a readership is really what blogs are about.
As for concerns about specific publishing rights, that is best put aside until you've been offered a contract from a reputable publisher, not before.