While this is completely off topic, I will entertain this for fun.
Actually, doing that would be perfectly ok, and not entrapment. There is a thin line, however. This would have to operate in the form of a 'sting operation' by SE. In this, it would be perfectly ok for them to create a dummy website and set people up in various zones to shout. In this scenario, the people who go to them to buy gil are people who would have done so, as there is no direct provocation on the part of SE in this scenario.
This is no different than how cops set up dummy prostitution ads on sites like backpage and craigslist; or how law enforcement sets up in teen/child chatrooms to catch pedos. They don't go in and provoke the act. They simply place the bait, and people who are out to commit the act will take the bait.
Entrapment involves initially enticing people directly and individually, and provoking illicit activity. So there is a difference in what AnimaAnimus was talking about and entrapment.
*For an added piece of information. If you do take the risk to participate in illegal activity with someone. You should know, if you ask the person if they are affiliated with law enforcement, and they say no...that is NOT entrapment. The same would go for SE if they were running sting operations. Undercover operations are undercover for a reason; so they can catch people who intend to take part in illicit activity. People who do not intend to commit an illicit act will not be caught in these kinds of situations.
Your idea is actually fine, there is nothing wrong or illegal about SE doing sting operations. I would honestly be more surprised if they were not doing it already. You really never know, no matter what they would tell us here.