Now you can convert the fake messages to regular messages: just star the ads and they are saved to your inbox as messages received from firstname.lastname@example.org. "New! Starring Ads. Starred ads will be saved to your Promotions inbox," informs Gmail. While the messages are added to the Promotions tab, you'll also see them in the Primary tab because all the starred inbox messages are added to the Primary tab by default. You can unstar the messages, delete them, archive them (just don't send a reply).
This screenshot allows you to see both the ad and the message created from the ad after starring it. The ad is removed after a few seconds, so you don't get duplicates.
Here's the ad:
... and the message created by Google:
All the sponsored promotions that are available for your account can be found at: https://mail.google.com/mail/#pinbox.