Oxford Living Dictionaries give this among their examples of gender-neutral they:
‘I mentioned this to someone at work today and they looked at me as if I were a space alien.’
In a usage note, Oxford comment that, recently:
they is now being used to refer to specific individuals (as in Alex is bringing their laptop).
Your question was, in effect, whether gender-neutral they was acceptable in "educated speech" in cases where the gender of the referent is already known - as in Oxford's example above.
In my experience, the answer is yes.
Still, there remain some who would criticise such usage, as the other responses to your question show. Even in contexts where the referent's gender is unknown, there are prescriptivists who would prefer to avoid they, though their number and influence are undoubtedly diminishing, and on the whole they are more likely to object to written use than to spoken.
(I agree with user3169 that the first two sentences would sound more natural in the plural, and I also agree with Ermintrude that even if those two sentences are left as they are, they are less likely to raise objections than the other two, because the listener might interpret "them" as shorthand for "the girls" or "the boys" rather than as a gender-neutral singular.)