In 2014, I’d argue that a business refusing to have an online presence is the same as refusing to have a telephone.
Is it possible? Sure. If a customer really wants what they’re selling, they’ll have to show up in person. If they’ve decided to invest in a brick-and-mortar location, that is.
I recommend to all my clients that they first establish a website, followed by an email list. Then they should branch out to those social media platforms where their customers are, but only if they’re prepared to invest efforts there. Otherwise, it’s like setting up a telephone number that you never intend to answer. That makes the business seem unresponsive at best, perhaps even incompetent and uncaring.
If customers are beating down a business’ door, great. Otherwise, it make sense to be prepared to use the same methods of communication their potential customers use.
1986 called. They want their marketing plan back.