It's not that I can't understand the ironic intent (after all those years studying Ironic Theology I ought to). And you might want to read Simon Jenkins's blog on the matter. But there's one fatal flaw, in my mind. To illustrate, imagine a bus stop on a Home Counties former-council-estate:
Small, sweet girl (sorry, it probably won't be a boy. It's a doll.) : Ooh! Look! What's that!
Theologically uneducated mum: I dunno, it's a bit scary... Godbaby?
Girl: Can I have a Godbaby for Christmas?
Mum: I don't know. There's no price on it, or where to buy it.
Girl: But I love Godbaby!
Mum: Yes. But we'll have to see if Santa can afford a Godbaby.
Girl [sobbing]: Want a Godbaby for Christmas!
Mum: We'll have a look on the Argos site when we get home.....
So follows an evening looking at Argos, Tesco Direct, JLP, Hamleys - all to no avail. In desperation Mum follows an obscure Google link she's been avoiding all night, to a Church website.
Mum: Amelia (or, as it may be, Rose or Sarah-Jane or Jamie) - that Godbaby....
Girl: What? You've found one?
Mum: I'm sorry, no. You see - the Godbaby doll doesn't exist...