WLC: "You can't prove the negative"

[Belacqua]

The Early, Middle and Late Dialogues, yes, and, of course, The Republic.  In the latter the statement is found, "If the gods exist...."  

OK, so you'll know that while Plato writes about the gods of Greek mythology, he feels no need to describe them in agreement with Homer or Hesiod. Think of the Symposium, where each speaker describes Aphrodite or Eros very differently, to make his own point. This was not considered blasphemous or scandalous. As far as I know, whenever one of the named Greek gods appears in Plato it is used in this symbolic way. 

In the Phaedrus, you'll recall, he is noncommittal on whether the myths about the gods are true. When asked, he tentatively suggests a euhemerist explanation, but says he doesn't really care -- he'll leave it up to the experts. Here he says very explicitly that he uses the stories of the gods as symbols to think about his own character. The words you cite from the Republic also indicate that he is noncommittal.

In the Timaeus he suggests that a Demiurge made the world, but this is a craftsman, and the Forms are above him and determine his work.

Plato clearly believed that the Form of the Good was above the Demiurge, and served many of the functions that Christians later attributed to their God. Whether Plato himself would have called the Form "God" is not entirely clear. Experts who know a lot more than I do disagree about this. 

We can be sure, though, that although he speaks of the polytheistic pantheon of Apollo, Aphrodite, etc., as small-g gods, he also sees a higher, immaterial, unchanging Form above them. It's not clear whether Plato meant this in the way that Plotinus meant the One, but by the time Plotinus was writing that's what it had come to mean. 

The relationship is pretty similar to the Hindu pantheon, in which Shiva and the other higher characters are called gods, but above them is an eternal unchanging ground of being: Brahman. So just because you have characters running around called gods doesn't mean that you don't have something quite like the One over them, containing and determining all of existence. 

So I find no evidence to think that Plato believed in the polytheistic pantheon behaving in ways that Homer described.