On StackOverFlow, the users who do not put anything in the profile have this displayed.
"Apparently, this user prefers to keep an air of mystery about them.".
Should it not be him/her?
Clarifying before hand that English is not my strong point.
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
Yes, it's correct. English literature is full of examples of them used as a gender-neutral pronoun, even when referring to one person. It's also a great way to refer to someone when you don't know their gender, or when you don't want to favour one or the other, e.g.:
"When our next customer walks in, please greet them."