A recent study by Google research demonstrates that paused search ads due lead to a reduced number of visits to targeted sites that can not be made up for by organic search traffic. Their study measured clicks based on a reduction in search advertising from a paused advertising perspective (zero dollars spent) vs. increased amounts being spent.
Basically, Google is telling us the dollars we are spending on search advertising work. Review the infographic and you'll see how those dollars can work for you. The results of the study come from almost 6000 cases. So if you're wondering if the advertising matters, it does.
Now, does Google have a biased perspective on this stuff, hell yes! They are the people selling you the advertising space. Regardless of that fact, the figures show, it matters. Allowing your products and services to go without an ad campaign will hurt you. It's a nice inforgraphic on a difficult topic to pin down. Weeding out the variables that account for search traffic is a task all its own, so enjoy their work and take advantage of the findings.