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?
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.
Someone may come up with a quotation that proves me wrong, but this is how id answer off the top of my head.
Palpatine is the product of Darth Bane's "Rule of Two" (bear with me, im trying to explain the passing down of knowledge between KOTOR and TPM).
During the KOTOR era, Darth Bane realized that the Sith could never defeat the Jedi in a full blown war of two military forces because the Sith dogma called for apprentices to kill their Masters to ascend the ranks, leading to constant in-fighting and an inability to form sufficient leadership. Instead, the Sith must be changed to be defined as 1 master and 1 apprentice who use their cunning and patience to find the correct moment to strike at the entire Jedi Order and wipe them out in a single action (Anakin and Sideous, Order 66).
Since Bane went in that direction, and the Sith masses were fully defeated shortly thereafter, the Jedi retreated back to an era of stagnation on their core planets, and left virtually all knowledge, Jedi and Sith alike, behind (just like what had been done before in the era of Marka Ragnos and the other old Sith Lords before the Force Wars broke out).
As part of Darth Bane's rule of two, im sure that basic knowledge of the former Sith Empire was passed down from Master to Apprentice over the years, but details like Dromund Kass being a former Sith core world almost assuredly was not passed along.
This tendency for the Jedi/Sith to get distracted and forget everything every 10,000 years drives the ongoing quest for young heroes/villains of going on journeys to find Jedi/Sith holocrons and unearthing long lost knowledge.
I don't think he knew about Dromund Kaas but he almost certainly would have known about the Sith empire. It is probably in historical records of course he would have about as much detail about it as we have about say the 100 years war. He would have known about it as an opposing force that made war with the republic. And the war couldn't have been kept secret since the empire destroyed the Jedi temple. He might not have even known that it was a Sith Empire he just would have known that there was a huge war some 3000 years ago (that number might not be accurate) and that the enemy nearly destroyed the Republic.