Simply put, no. It's almost entirely made up
In their album "War of Wrath", Blind Guardian decided to tell the story of The Silmarillion in a chronological order, with a narrator telling the story as it's told in the book. However, they opted to open the album with the end of the story and the War of Wrath. The most telling factor that it was made up was the remorse that Morgoth seems to have for the actions he caused. In particular in the final lines of the song:
I left ruin behind me when I returned. But I also carried ruin with me. She, the mistress of her own lust
This is very unlike Morgoth. Morgoth cared not for the destruction he caused, in fact he relished in it. This is one of the few things that separated servant from Master. Where Sauron was obsessed with domination, Morgoth was obsessed with destruction.
While the conversation itself was made up as very limited details are given of the War of Wrath, some of the lyrics do appear to have been inspired by the writings in The Silmarillion.
For example the line The enemy is within, everywhere. And with him the light and There are places below.
Then the sun rose, and the host of the Valar prevailed... and the might of the Valar descended into the deeps of the earth...
The Silmarillion, Chapter 24: Of the Voyage of Eärendil and the War of Wrath
As well as the following line: There are places below.
He fled into the deepest of his mines
The rest of the arrest of Morgoth goes as follows:
and sued for peace and pardon; but his feet were hewn from under him, and he was hurled upon his face. Then he was bound with the chain Angainor which he had worn aforetime, and his iron crown they beat into a collar for his neck, and his head was bowed upon his knees.
This also seems to be supported by this review of the album heavyblogisheavy.com (Emphasis mine):
You see, Blind Guardian do a lot more than simple reference, taking segments from The Silmarillion and copying them one by one. Instead, the band offer their own interpretation, both in which parts to display (like the almost complete absence of Men or the focus on the Noldor) and how to display them (like the editing of Feanor’s speech or the focus on “Day shall come again”, only a part of the closing moments of The Silmarillion proper, here given almost a solitary, summary role). This makes Nightfall more than just homage, elevating it to the realms of reinterpretation and analysis.