Checking the CMB against it is FAR FAR FAR FAR more likely to get a hit... Even then, it's not likely, since canon says you can't detect an operating BG with passives except by star occultation... which implies it radiates at/near CMB levels, BTW...
Don't forget the 'flicker rate' settings.
You don't have the globe running 100% of the time, you cycle it so many times per second so that some radiation escapes the ship, and if your computers calculate it right, you get enough radiation from your ship, or background passing through the globe, that it doesn't look much/any different from the background radiation to the hypothetical observer.
It also lets your ship build up a passive sensor picture of what's outside the sphere.
I thought it was rather clever when I read it, no idea if it would actually work since I didn't think any given ship of the Imperial Fleet would actually radiate long wave microwaves. But it's listed as a tactic of the black globe ships.