Some would and some wouldn't depends who they have as customers. I worked in a shipyard who never advertised in almost 100 year yet had plenty of work. We were listed in marine yellow pages and phone book but no other advertizing. Anyone with a ship knows where the shipyards are and reputation matters. I am sure other business have as little need for advertising. My brother and his wife had a business for many years with no advertising, they didn't want more work than they could handle.

it is possible but not a guarantee. It depends on what happens to sales over the long run and exactly how much they were spending on advertising. If they spent a large sum of money and it wasn't very effective advertising they might not lose that much sales and profits might actually go up.

If you don't know what the product or service is that the business is selling would you spend money there? Advertising dramatically increases awareness which translates into sales.

Yes it's very obvious they would lose money if they stopped advertising!

If they have no competition and are the sole supplier of their product, then advertising may not be as essential, but in competitive fields and products with limited inherent value like some supplements and sugar water their sales are clearly the product of their advertising.

Maybe, maybe not. It all depends.