GRMA, a Scilling. Good to see the examples. I'm used to the uses of ann in statements, but have never knowingly run across it's use in existence questions. In that same reference you gave are others like Cé atá agam ann? = "Who is it?" and Cé seo agam ann? = "Who are you?" Strange, but lovely, like the language itself.
Is it a word that enriches the meaning somehow, but could be left out and the sentence would still make sense? (kind of the way Québecois French often uses "lá", as in the examples here: http://offqc.com/2013/04/30/everything-you-ever-wanted-to-know-about-the-quebecois-use-of-la-594/)
It looks like you are replying to scillings response, so it's not entirely clear what your question is - what "it" are you talking about when you ask "Does it incorporate the ann somehow?"?
Ann is used in what might be called existential statements and questions, so the FGB has examples of questions like cad is pósadh ann? - "What is marriage?" and Cad is grá ann? - “What is love?”, and statements like Tá Dia ann - "God is", Tá lá maith ann - "it is a good day" and Tá an t-earrach ann - "it is spring".
Tá Dia ann might also be translated as "There is a God, but it's not a positional "there" - other examples cén plean atá ann inniu?, "what's the plan for today?, or cén seans atá ann go dtarlóidh sé? "what's the chance that it will happen?", where you could also translate them as "what plan is there for today?" and "what chance is there that it will happen?"
The question referenced is the original "Cad is aire mhaith ann?" that scilling translated as “What is in it, good care?” I think your answer addresses it adequately, though. Going off of what you're saying, a response to "Cad is aire mhaith ann?" might be (in reference to say, a nurse right in front of us being a good example) "Tá sí sin aire mhaith ann." Yes?
Actually, no, I don't think you would respond to Cad is aire mhaith ann? with Tá sí sin aire mhaith ann
For a start, you wouldn't respond to a copular question with tá - you might say Is aire maith í sin but that's a rather direct answer to a more nebulous question, and you don't need the ann in that answer.