You've repeated this in a few places in the last couple of days. Can you please provide your source for the dragons not being able to consume divine magic?
We know this because God Magic CANNOT be absorbed by Dragons, in fact it is shown to be anathema to them. And we know Balthazar was not a God, or did not have the magic that made him a God, during all of this because we didn't go blind looking at him.
As for Balthazar, whether he qualified as a god or not is impossible to say without knowing the exact criteria for divinity (which we don't). The explanation could be that there is some kind of fundamental "divine essence" which carries an inherent property of blinding mortals, and Balthazar is lacking this so no longer a god, but there are other alternate explanations that could fit the facts too.
For example (just suggesting something possible here, not saying I necessarily agree with it): the other gods took as much of Balthazar's magic and power as they were able to, and in his weakened state he isn't radiating enough energy to cause blindness, but they didn't strip away anything fundamentally divine, and their claim that he's no longer one of the Six is intended as a statement that they've rejected him as one of their fellows. (The exact wording "Balthazar has been stripped of his claim and his title. He is no longer one of the six." certainly seems less like an implication that anything has physically changed about him. And in the case of Abbadon, despite being imprisoned by the others and no longer considered part of the pantheon, he certainly retained his divine status.)
For all we know, there might not even be such a thing as "divine essence", and a god might just be someone who contains a massive amount of regular magic. Without more concrete information about what the gods are, how they work and how new gods are made, we can't say anything for certain.