You can either re-render the whole textarea by a4j:push or pass some data to the client using "data" attribute and then append it by "oncomplete" script.
One of the tricks to trying to find answers in a technology you're trying to learn is not knowing what exactly to ask for.
Thanks for corretly deciphering what I was looking for. I found Ilya's blog post here:
that I believe provides a good hint on what I may need to do. Thanks for your help!