Judging from history, religious organizations tend to go underground when confronted with a government that does not tolerate their beliefs.
They also sometimes emigrate in large numbers. As examples of this, see French Huguenots, Mormons in the US, or Jews leaving Germany, Russia, and various Arab countries.
If the dark empire was smart maybe they would try infiltration or some other method rather than brute force, but in the end I can't think of an example of any government successfully forcing any group to stop in their beliefs. The odds of an atheist government doing so are even more slim than most historical examples because the atheists do not have a substitute belief system to offer.
I can't come up with many examples of groups totally eradicated that had a significant presence to begin with. However, it's not unheard of for groups to be heavily discriminated against and forced to leave in large numbers. It's not always going to be permanent, but it may well last for decades or generations.
It's also not exactly fair to say that an atheistic group doesn't have a "substitute belief system" -- they may actually have a reasonably coherent one, but it might explicitly deny the existence of any supernatural or divine entities, and instead draw strictly from humanist philosophies. While atheism is sometimes strictly an oppositional rejection of another belief system, it's also possible to define a set of guiding principles that has nothing to do with any sort of suprahuman entities or knowledge. It might not be the kind of thing that present-day people would find comfortable or familiar, but it can be done.
For one possible example... think of a culture that believes there is no existence beyond this one, and that the only way to honor the memory of those past is to make the lives of their descendants richer and easier. They might take a very expansionistic view of their place in the universe, and consider waste, pollution, and inefficiency to be disrespectful of the resources bequeathed to them by their forebears. Obviously, this would need to be fleshed out, as I'm just spinning this off the cuff, and there would be consequences I won't get to before it's time for supper, but that's a start. It could be a culture that completely rejects any an all forms of traditional religious belief (unless you consider "ancestor reverence" a religious belief), and it doesn't define itself in relation to any other culture.