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.
That may be correct if every company spends similar amounts on traditional advertising, but this isn't true. In reality, such a tax would hit companies with larger traditional advertising budgets harder, and make some companies choose to shift some of their marketing spend to other communication methods.
For example, I work for a company that has a small advertising budget with no traditional advertising. We have a website, publish papers, and occasionally have a booth at a conference. Some of our competitors have significant advertising presence in trade magazines, social media, news sites, etc. Therefore this tax would impact them more than it would impact us.
More importantly for the purpose of the tax, it might shift our competitors' behavior. Ad buys that were of marginal utility to the company before would be even less cost-effective so either advertising platforms would lower their prices or the company would not buy the ad. In some cases this lower price would make it no longer profitable for the platform to display, eliminating the ad enteriely.
But most ads you see are for consumer products. Coca-Cola, cell phones, soap and shampoo, cars, fast-food brands, toys. These don't have anywhere to shift to. Dove soap isn't going to switch to reaching people by newsletter. They'll just pay the tax and pass on the costs to consumers. The vast bulk of advertising simply wouldn't change at all.
And like I said, even with a slight drop in demand, the main effect would be to lower advertising prices, not reduce advertising space.