Does Share of Search correlate with Revenue
Absolutely, it is an investment.
Any time money is put into something with the expectation of earning more in the future, it's an investment.
The challenge, as Dale W. Harrison points out, is that marketing, like a factory or any other asset, only delivers results if other elements are in place. It's a metric issue, where isolating marketing's unique contribution is difficult. But this applies to all investments. For instance, hiring 50 salespeople won't generate revenue if there's nothing to sell—salespeople leverage the product.
No investment generates revenue independently, except those that are inherently broad, like buying stocks. So here, you need a metric system that correlates to revenues.
Download the validation study for the Tourism and Spirits industry