Wouldn't that...end the universe? Or be redundant...
Depending on what theory you go with it should do one of two things:
a) TWG is summoned and due to the simply insane, unfathomable power it breaks reality and everything goes back to the way it was before creation started.
OR
b) Nothing happens as TWG is literally everywhere already, and therefore was already there the whole time, which means TWG is everything i.e. Creation.
If an avatar was summoned that's all it would be. An avatar. Similar to summoning one of the Queens when trying to summon Winter itself or something like that. Arguably, the being that is most likely to show up is the Metatron, being the Voice of God. An angel or perhaps not an angel. Depends on how you look at it. Alternatively, an Archangel might show up.
I'd doubt Jesus or some other mortal avatar of TWG would show up. It's possible, but unless you meant to summon them deliberately I don't see why they would appear. Nothing at that level happens by accident. You get whoever you're meant to get.