Raven, you're confusing the Borg with the Jem'Hadar. The Jem'Hadar are the ones who serve Nurgle.
The Borg were raised from the cold depths of the earth by the C'tan, who wish them to seal the Materium off from the Immaterium by destroying all life in the universe.
I don't know about the Jem'Hadar. They are servants of the Changelings, which are obviously Daemons of Tzeentch. So unless they are using the Chaos Undivided rules, they would be mixing up the Chaos Gods.
Being disfigured as they are, I suspected the Borg were servants of Nurgle that had corrupted a rogue sect of Techpriests who have completely given themselves over to the Machine Spirit.