According to a recent article in Slate Magazine, no.
Ebay ran a country as a control group, running no paid search. What they found was that their business did not decline at all. In fact the business stayed the same. Users that wanted to use ebay and their services found them anyway.
Internally we still augment our organic search results with paid search but the best, most qualified leads we get are those generated organically. Why? Because people seem to have trust in organic results. Maybe because you earned it. Users are increasingly becoming savvy and know that you don’t just appear at the top of natural search with out your product or service being highly relevant.
Instead of paying all that money to search engines, why not invest in organic search. Not only will your search results yield better conversions but in the process of building your search campaigns you will be writing better content for your users. This content can help turn prospects into customers.
Finally, with a good SEO strategy, social media will improve. Again, building more, longer term customers through shared voice.