If you're asking whether advertising works, there is plenty of science making clear that it does, without fishing for anecdata.
As to whether every company buying ads is making a good investment, mileage may vary - but the blunt answer to your question is that yes, people do purchase things because they saw ads for it, the advertising economy is well understood. Companies like Google whose fortunes rest almost entirely on the known efficacy of advertising are not full of idiots who have never thought about whether or not ads actually work.
"Is an economy based on selling attention ultimately the most beneficial and productive one for all participants" is a separate question, but it's not the question you're asking.
> there is plenty of science making clear that it does
Funded, ran, and interpreted by whom?
I can't remember the last time I bought anything just because of its ad, that I already did not know about or was going to buy anyway, nor I know anyone who did.
In fact, if I see an ad TOO often, it permanently turns me off the product or service.
The whole ads racket seems like a case of an emperor with no clothes at best, and a thin veil for mass surveillance at worst.
One day you'll need to buy something outside your sphere of knowledge; a washing machine, drain cleaner, car tyres, whatever. The seeds of biased selection have already been implanted by years of conditioning.
