I'm afraid I can't give you a peer-reviewed answer. However, the use of the singular "they" by Shakespeare is well documented.

NYUlocal's discussion of the Swedish "hen", also claims the singular "they" was used in The Canterbury Tales, Hamlet, Mansfield Park, and The Universal Declaration of Human Rights.

More to the point, in "A Comedy of Errors Shakespeare uses these lines:

There's not a man I meet but doth salute me
As if I were their well-acquainted friend

And there's this from "The Rape of Lucrece":

Now leaden slumber with life's strength doth fight;
And every one to rest themselves betake,
Save thieves, and cares, and troubled minds, that wake.

I'm afraid I can't give you a peer-reviewed answer. However, the use of the singular "they" by Shakespeare is well documented.

NYUlocal's discussion of the Swedish "hen", also claims the singular "they" was used in The Canterbury Tales, Hamlet, Mansfield Park, and The Universal Declaration of Human Rights.

More to the point, in "A Comedy of Errors Shakespeare uses these lines:

There's not a man I meet but doth salute me
As if I were their well-acquainted friend

And there's this from "The Rape of Lucrece":

Now leaden slumber with life's strength doth fight;
And every one to rest themselves betake,
Save thieves, and cares, and troubled minds, that wake.