God has used unbelievers to do his will throughout the Bible, and I'm sure he can use "unbelieving music" to do the same. He is the Lord of All Creation.
- God used Pharoah to have his heart hardened so that he could inflict the 10 plagues, and allow the Hebrews to take silver and gold when they left Egypt.
- God used the nation of Babylon to teach his people and bring them back to him, and even gave that prophesy to Jeremiah.
- Cyrus King of Persia ordered a Temple to be built in Judah because God had given him the kingdoms of the earth.
- God used Abimelech to teach Abraham, as well as provide for him.
- In the story of Esther, God used Xerxes to save the Jews from destruction.
- Even under captivity, God used the Roman centurions and captors of Paul to carry out his will and message, such as on the boat in the storm.
Yeah, so I think God can use a Jazz chord to do His will, even if people believe it isn't of Him. If He can use the King of Babylon, Pharoah, Abimelech, and Roman Centurions, He can certainly use a dominant 7th chord or wayward muscian to build his kingdom and work His will.