It depends on the business. I own an S corporation that I started in order to take on one customer. I have no plans on this corporation ever taking on new customers, so no advertising is necessary. No one knows this company exist other than the company who has a contract with it, the IRS and myself. Occasionally, I get a piece of junk mail addressed to the corporation, so I guess there is a way too look up any registered business, but I would not call that advertising.
There are thousands of corporations that are set up for specific purposes that advertising serves no purpose.
There are also businesses that have no intention of surviving. I know people who set up a corporation for a single event that are dissolved immediately after its purpose has been fulfilled, even if it is for just one day. Those businesses often do not advertise.
I have had to start a corporation to bid on a contract that I didn't get, so I dissolved it right after the bidding period ended.