Businesses will just continue to advertise, and pay the tax. Because all their competitors have to pay the same tax, it's just a status quo. And businesses will raise the prices consumers pay to make up for the difference.
So ultimately it would wind up being a regressive tax, like tariffs, paid for by people in rising consumer prices.
Taxes can only deter behavior when there are alternatives. But there aren't alternatives to advertising. Businesses advertise because it works, because it increases their revenue.
Also, if taxes did slightly reduce demand for advertising, then the price of advertising would just decrease, that would be the main effect. There would probably be a tiny contraction in advertising space, but not enough that anyone would notice.
The main effect would be to raise prices for consumers, not to reduce ads, because there aren't substitutes for advertising.