So, my theory is, if how you came to write the book, or who you are is an interesting story it'll be more memorable & more likely to translate into sales.
I cover books for a regional alt-weekly newspaper (with website), and I agree.
We don't run "This guy published a book" pieces; I vet everything. But we do write about self-published books if they fall into one of two categories: 1. Fiction, essays or poetry written on a truly professional level — these we review; 2. Nonfiction with a good local story attached — this might be a feature.
In terms of effect on sales, I only have anecdotal evidence. A local indie bookseller told me he had seen greater demand for books I reviewed. (Most of these aren't self-published, though.) Occasionally a reader will write me asking to be reminded of the title of "that book about the German kid who sheltered a Jewish kid during WWII," or whatever, because the description apparently stuck with them.
We have had local self-publishing successes, but they're mostly due to the authors' relentless promotion of hard copies, not to press coverage. I know an author who's sold about 10K of a lighthearted nonfiction book by getting it stocked at gas stations, general stores and other atypical places. (It works because of her strong, humorous local angle.) I know another who has a great platform (local actor doing one-man shows) and carries his books in his car trunk ready to hawk them to everyone he meets.
If you do approach a newspaper, it's good to know what kind of book coverage they do, if any. Many daily newspapers no longer run reviews, but ours occasionally rounds up books (including self-published ones) and blurbs them. (The blurbs basically just say what's on the back cover.) We try to do substantive coverage (meaning: I actually read the book), but we lean heavily toward the literary. You may have the next
Chicken Soup for the Soul, but that's not a good fit for our audience, so you're better off pitching it elsewhere.
And if you get a good review, by all means, tweet or blog it. There's a best-selling, trade-published local author who gets reviewed in all the big papers and still bothers to tweet my reviews, because no press is too insignificant for him to care about. (Of course, he also has a ton of followers...)
ETA: I wonder if there's been an increase in the number of people who read newspaper reviews online and then go directly to the e-book, making the presence of books on shelves irrelevant. Around here, most people still seem to prefer print. But I've certainly read about interesting titles online (at AW, among other places) and gone directly to iBooks to get a sample — it's just a few clicks away, after all.