It depends on which shit-weasel was going to end up running the region.
First of all, Rosenberg didn't know shit from apple butter when it came to the Caucasus. He was a Baltic-German, and while he could wax poetic about personal experiences in "The East," he really could only speak to the Baltics as a half-ass expert. But there were Nazi Party Caucasus-Germans with real life experience in the region and some of them were in position of power and could effect policy on some pretty scary results.
The other thing, nobody in the Nazi Government took Alfred Rosenberg seriously after a while. He had the unerring ability to piss off everyone around him, including those who professed to share his worldview, but different people had different time-limits of being able to deal with him. Some could not stand him after meeting him in five minutes, other had the patience to last five years. Hitler was in the latter category. And Hitler was prone to monologuing about everything and anything as the mood struck him. Some monologues were consistent. Others were contradictory. Which meant Hitler's views were only translated into actual policy if someone bothered to write it down and then pass the message along if suited their interests. That was the truly terrifying effective power of Bormann, jotting down all these Hitler after-belches and then showing some of them as Hitler's Official Government Policy to functionaries with Hitler nodding it through.
Add to this witch's brew of awful: SS and the Army. There is no way Himmler, pedantic and myopic as he was, would not see the potential to exploit a region with oil in it. And also, bright boys in the Army would have wanted a say, and as the Victorious German Army Fighting the Greatest War the German People Have Ever Seen, they would had a say. How much? Well, that's also debatable.
The unsatisfying answer is that "I don't know," but I would not read too much into Rosenberg. Hitler certainly didn't.