I guess such a topic, while related to both psychology and hacking, is essentially belonging a site like this.
On the other hand, it would not be the best idea to give people advice for morally questionable acts.
What about this topic?
It should be on topic (but we shouldn't teach people how to do it).
Social engineering is defined on Wikipedia as
Social engineering [...] refers to psychological manipulation of people into performing actions or divulging confidential information.
It clearly is a set of interpersonal skills and as such should be on topic.
Social engineering is not necessarily nefarious. Getting a store clerk to accept your return and give a refund, or getting a (larger) compensation for an inconvenience you've suffered, can also be called "social engineering". This should be on topic.
And when it comes to social engineering of the nefarious kind, asking how to defend against that should also be on topic.
If you ask a question "I want to hack the Pentagon, how do I do that?" on Stack Overflow or Information Security, it would very likely be closed right away. If a question on this stack would ask "I want to get someone's password, how do I do that?", I hope the same would happen.
But the techniques used are just general interpersonal skills, which can be used for good or for bad, and they should be on topic.
Social engineering, the process of getting information (passwords, for example) from people that they don't want to give, should not be on-topic. If the question is in the context of computer security, it should go in that topic-specific SE.
The more general topic of "how to manipulate people against their will" seems on-topic to me, but I have concerns about promoting questions asking how to do unethical behavior. The question of morality is probably a separate meta question.
There are some highly negative aspects to social engineering. How to do it should be off-topic for this site. How to defend against it is what should be on-topic.
So let's be clear about what the most common definition of this topic is. A quick search of the Internet shows basically the following (allowing for variations for a topic that probably morphs over time).
As I understand it, social engineering is:
So it boils down to a simple concept: Are we here to help people or to hurt people.
You may want to say that I will trick people (socially engineer them) for "the greater good". You are still tricking them. You are still manipulating them. So you are saying that the end justifies the means. I'm sorry, but I will never trick someone because my "superior intellect" dictates that it is for their own good.
This site should be about helping people. If we want to do that as a community, then when it comes to social engineering, we should help people to recognize and avoid/prevent its detrimental effects.
How to conduct social engineering on another person. NO.
How to detect, guard against, properly react to social engineering. YES.
Wouldn't any really blatant attempt at:
How do I get [person] to do [x] against their will?
... pretty much immediately fall into the category of 'too broad' and be closed appropriately? I hope it would be, because that would almost certainly apply here :)
If you're really on the lookout for something possibly sinister, as in someone actively trying to do this, you're going to be spotting for someone working through questions on earning trust, and other much much narrower things. I don't think any serious attempt at social engineering (as in, how to do it to someone else) would actually come to light here.
What are tricks I can use to quickly recover a talkative audience if I'm speaking in public? That's pretty benign, but still social engineering depending on how I ask it and how you interpret it.
For now, I recommend allowing it, and seeing if an actual problem comes to pass. If one does, then you have a real world example to discuss, and the problem stops being imaginary or theoretical.
I think the possibilities are just too many for a blanket "yay or nay" here.