If not, you're talking to a very articulate thick-headed person who can argue you into a corner by deploying all manner of argumentative/persuasive patterns, but may never try to reach across the table for a compromise.
If anything I'd go so far to say that LLMs are innately more vulnerable to persuasion than humans are, they are technically just a complex text completion algorithm at the end of the day after all. Even with the strictest system prompt, the best they can do when cornered is bend the knee, devolve into a pattern of verbatim repeating themselves or just start spewing a bunch of gibberish in the worst case.
In reality stubborn thickheaded folks who refuse to compromise are pretty much the norm across social media in my experience, so even if LLMs really are capable of what you're suggesting here I don't believe there would actually be much of a difference to the status quo.
While it might present a save menu similar to the real game, that doesn't mean the menu itself actually functions. With LLMs, they are ultimately only able to remember what's been pre-trained into their model + whatever is discussed within their context window.
A hypothetical LLM based online bot/shill sent out into social media would likely be including the entire discussion within their context window for each post generated though, otherwise it wouldnt really be possible for it to maintain a coherent conversation.