Spredfast.com offers a report about small business publicity in which over twice as many (79%) depend on word of mouth (WOM) to promote their business than social media (35%). Businesses use advertising almost in between at 44%. The Hiscox Small Business Survey also small businesses offering IT/media services or business services were much more likely to use social media as, say, auto repair shops.
Authors with one book are also small businesses that need to promote their product. My sense is that authors are more likely to utilize social media. This may be truer of younger authors than older ones, of course. Yet, all authors may rely too much on word of mouth or advertising and not enough on social media, especially at the duration of the writing process and the start of publication.
Notice, especially, that word of mouth is not a tent pole for developing your author platform. Advertising can be, but it relies solely on the author to layout the cash for this.
Notice, also, that including a robust social media plan in your book proposal may make you stand out from the crowd of those who avoid social media.
In sum, do more than word of mouth when planning or executing your publicity and promotion.