Does advertising distort our economic system?
In economic terms, it is not.
Economic distortions are things that come in from outside a given economic transaction, making actors do things they would not otherwise do. These include things like government taxes and subsidies. Let's say that I would not ordinarily purchase auto insurance. If the government tells me I must, it creates a distortion where I do something I would not otherwise do. The government is not part of the economic transaction, but it causes that transaction to occur.
By contrast, the advertiser is part of our economic transaction. The advertiser is trying to persuade me to voluntarily buy from them. Therefore, if they succeed, they have not induced me to do something I do not want to do. Instead, they have changed my mind and caused me to want to do that thing.