Daniel 3:19-27 – Who is the Fourth Man in the Fiery Furnace?
Daniel 4 – Is Nebuchadnezzar’s Madness Historical?
Short answer: no. But, as Phil notes, there is a very good case that the story in Daniel four is a garbled account of an event in the reign of his successor, Nabonidus, the last king of Babylon. We know from Nabonidus' own inscriptions that he was a devotee of the moon god "Sin." This was a point of conflict between him and the powerful priesthood of Marduk, the chief god of Babylon.
Nabonidus was away from Babylon for ten years, residing in Teima in North Arabia, which was a center for the worship of the moon god. In later Babylonian tradition he was remembered as a madman.
Again, as Phil notes, among the Dead Sea Scrolls was discovered an Aramaic fragment of a work we call The Prayer of Nabonidus. It tells a tale that involves Nabonidus, not Nebuchadnezzar, and it reads like an intermediate version between the inscriptions of the historical Nabonidus and the tale in Daniel 4. You can read a translation of it in Phil's post
I think of both the Prayer of Nabonidus and Daniel 4 (and Daniel 2-6 in general) as examples of what I call "Aramaic Fantasy Babylon." Like Greek Fantasy Babylon, this is the imaginary Babylon described by, in this case, Aramaic writers in the Persian and Hellenistic eras. I infer that there must have been a substantial Aramaic Fantasy Babylon tradition, although less of it survives than the fantasy Babylon of the Greek writers.
One other example of Aramaic Fantasy Babylon is "The Revolt of Babylon," the story of the unsuccessful revolt of Babylon from Assyria in 651 BCE, which is found in the Demotic Papyrus Amherst 63. This remarkable manuscript is a collection of Canaanite and Aramaic texts written in Demotic (late Egyptian) script. The revolt in this story was an historical event, but this Aramaic text tells a slightly garbled version of it which it fills out with imaginary dramatic dialogue.
Ctesias gives a lurid account of the same story in which the king of Babylon (Shamash-Shum-Ukin) pulls a Denethor at the end. He locks himself, his concubines, and his eunuchs in his own palace. Then he sets fire to a pyre and burns the palace down.
I have noted past posts in Phil Long's series on the Book of Daniel here and links.
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