Yes, this is exactly the point.
Advertising is most certainly a "negative externality." Its cost is not fully borne by the firm, but rather imposed on intermediaries and externals. For example, there is no cost to the advertising firm for promoting blatantly incorrect or dangerous statements that must latter be corrected through costly education.
See for example the statistics about sugary-beverage advertising, and how society must ultimately pay for the health consequences [1].
>You could, instead, possibly make the argument that advertising is a prisoner's dilemma.
Advertising is not an issue of prisoner's dilemma (in which two players who benefit from cooperation are driven instead by rationality towards destructive outcomes).
It is more similar to a problem with asymmetrical information, i.e. the "market for lemmons." All of the posts in this thread about how "advertising is helpful for bringing information to the people who are looking for it" are talking about the very few instances of advertising improving the efficiency of an information marketplace. Instead, the marketplace is full of "lemmons," i.e. instances of advertising that are not aligned with true information flow, but with manipulation. The ad market is like shopping for used cars. Use caution.
[1] https://www.hsph.harvard.edu/nutritionsource/sugary-drinks-f...