Does advertising create an increase in buying your product. That’s the most important question.
But yes, the question still is: does it raise intent or did the user already want the thing, googled it, and clicked on the first result (which is your ad, above the organic results that also lead to your online store)?
There is a role for advertising because Google polluted their organic search results with Ads making it harder for you to find what you want and forcing you to compete for the top Ad spot. I realize that I can only speak for myself, but I have never seen any evidence that advertising works and I've worked in ad tech.