Well, first off, Socrates never gets back to the risk of damnation as reason to act justly, at least not in Book II. He does develop the notion of social contract as the foundation of society by imagining the State from the ground up. From there he talks about educating the children because the State needs guardians who “unite in [themselves] philosophy and spirit and swiftness and strength.”  To that end, he wants children to be educated about the truth about God. Well, at first he says “the gods,” but then he morphs into discussing god in the singular. I’m not sure about the choice to capitalize. But he concludes Book II by deriving this about God, he is “perfectly simple and true both in word and deed; he changes not; he deceives not, either by sign or word, by dream or waking vision.” 
What to make of Socrates’ God? A part of the argument about God includes that God is only responsible for the good and humans are responsible for the bad, and thus God is not responsible for very much. This sounds pretty cheeky. And this understanding of God was posed literally as an attack on Homer’s and Hesiod’s stories, but seems to be an attack on religion of the day.
I knew that Dante and Milton influence our notions of afterlife. I wonder how much Socrates’ God influences our understanding of the divine. It is most notably different from the God of the Psalmist or the God of 1,2 Kings in that Socrates’ God is sterile and distant.