Q:

Did Palpatine or anyone in the Galactic Empire know about Dromund Kaas and the Sith Empire?

The question is pretty straightforward. But to expand on that, did anybody in the Galactic Empire know of those regions and if so, did anything of significance happen there?

A:

Palpatine almost certainly learned of the Sith Empire from Darth Plagueis. In the Legends novel Darth Plagueis, the titular character muses about Sith Lords who had attempted to avoid physical death: 

As evidenced by those few Lords who had managed to perpetuate their spirits after physical death—foremost among them Emperor Vitiate, who was said to have lived a thousand years—the ancient Sith had come halfway across that bridge.
Darth Plagueis, p. 181

Vitiate is, of course, the Emperor of the Sith Empire which used Dromund Kaas as its capital. Darth Plagueis thus knew about the Sith Empire, and he presumably told Sidious/Palpatine.
Palpatine also knew about Dromund Kaas. At some point, he discovered the Prophets of the Dark Side sect which was based on Dromund Kaas. It's not entirely clear how Palpatine discovered the planet and the Prophets -- it might been through Darth Plagueis or from the Battle of Dromund Kaas from the Clone Wars.
Palpatine sent some of his dark side adepts to Dromund Kaas to train with the Prophets, but he did not publicize the existence of the planet. The public evidently forgot about the planet again after the Battle of Dromund Kaas, so in general only very high ranking Imperials knew about the planet.

