For Plato the Apollonian madness as I remember it from the Phaedrus is the mania which the Oracle of Delphi has when she is possessed by the God.
As such it is still a Mania, one where the divine power of a God overcomes the rational soul. Which would seem at odds with Nietzsche's very 19th Century conceptions of a solar God of rationality and harmony.
Nietzsche was a Classicist and Philologist before he was a philosopher though, so he would have been familiar with the myths and references in Plutarch to differences in art and music between Apollo and Dionysus. But this was more of a thematic contrast than the binary dichotomy of opposites which Nietzsche paints in the Apollonian/Dionysian.
Eg, in Greek Polytheistic Religion, when Apollo vacates Delphi for the winter months, it is Dionysus who takes over the role as Patron God. The two Gods, both sons of Zeus are individually quite different, but also complementary, and Platonically speaking as Gods their providence can descend downwards to the world of appearances and share their providence in the form of a divine mania. The Mania of Prophecy from Apollo and the Mania of Ecstasy and the Mysteries of Dionysus are still both manias, and therefore not really as binary opposites as Nietzsche has the Naturwahrheit, the truth of Nature of Dionysus and the Kulturluge , the lie of culture of Apollo portrays.
So I think Plato is in the background for Nietzsche here. Classicist Richard Seaford in his book Dionysos writes that Nietzche was likely influenced by 18th and 19th Century German intellectuals like Winckelmann, Schelling and Bachofen in creating this kind of ahistorical view of Dionysus, which causes him to ignore the democratic elements to Dionysus worship.
As the God most widely worshipped in the Mediterranean world of antiquity, but who is rarely mentioned in the Homeric epics written for the Aristocratic warrior class, and whose worship was associated with slaves, including feast days where slaves were liberated and women, and in Rome as Liber was part of the Aventine Triad of the Plebian Class (Liber, Libera/Proserpina, and Ceres the agricultural Gods of the working class), Dionysus has democratic aspects which are at odds with the kind of aristocratic tendencies of Nietzsche.