Think about it. It's already been established that this version of the Crime Syndicate is in the animatter universe, where the Sinestro Corps is based. Now let's say a bunch of dominating psychopaths set up shop in your neck of the woods and could possibly infringe on your own domineering. Would you let it stand? Would you? Or you?
The enemy of your enemy would probably appreciate you helping out on an ass-kicking, so I don't see the Green Lanterns turning away even the CSA's twisted efforts.