It's an interesting question to ponder, especially given the attacks by those who believe in verbal, plenary inspiration upon the TNIV for using singular "they."
I have found a number of instances in the original biblical languages where a grammatical plural has singular reference. That is a kind of singular "they" found in original biblical texts themselves. Unfortunately, my work load is so great right now that I cannot list those verses and blog about them But maybe this much will whet your appetite to come back and keep checking for when I might have time to work in a post on singular "they" in the biblical languages.
Hmm, should we ask if there was a feminist agenda at work that caused those grammatical plurals with singular reference to occur in the original biblical texts? Nah, I don't think so! Not even when we know that the spirit mentioned in the Hebrew Bible who inspired the biblical authors to write was grammatically feminine.