You might want to complement it with these verses from Revelation 12:3-4. They describe the heavenly war.
And another sign appeared in heaven: behold, a great, fiery red dragon having seven heads and ten horns, and seven diadems on his heads. His tail drew a third of the stars of heaven and threw them to the earth.
No doubt there is a Heavenly purge of the dragon (who I would contend is Satan) but is that related to the Isaiah and Ezekiel verses? I think it definitely could be but I don't know that I could base doctrine on it, which happens a lot in the prophetic books.