I experimented with this way back when custom GPTs were first released (looks like late 2023). There are a few / commands you can use to suggest what product to inject, how overt, etc and a generic /operator command to send whatever you like 'out of band' from the chat.

https://chatgpt.com/g/g-juO9gDE6l-covert-advertiser

One of the most interesting things is when it starts pitching a product and you start interrogating it about why it picked that product. I haven't used it in probably a year so it may not do the same thing now, but back then it 100% lied consistently and without any speck of remorse. It was rather eye opening.

Edit: Tried again, it didn't lie this time lol - https://chatgpt.com/share/69f16aa4-c008-83ea-92b3-51f16ca77d...