I have not seen the show nor read the book, but am somewhat familiar with the premise and the "What if the Nazis Won" premise.

With Hitler still alive, absolutely. As Hitler was living out his final days in the Fuhrer Bunker, as fighting raged nearby, and then overtop, his bunker at a point was cut off from communications. Hermann Goering was one of the highest ranking Nazis, and was clearly in the running for being the next Fuhrer / President of Germany should Hitler die. HOWEVER, he had been sort of on the outs with Hitler the last couple of years of the War because he made a ton of promises about air supremacy, and yet he could not deliver. The Luftwaffe was virtually ineffective and non-existent at the end of the war. However, he still felt he was on top. So the bunker is cutoff, Goering is off at the Berghoff in the Bavarian Alps, planning on running a Nazi Government from there, since Germany was almost completely cut in half by this point. He messaged Hitler essentially saying that if he did not hear from Hitler within 24 hours he would assume the bunker had fallen and Hitler had been killed or captured, and he, Hermann Goering, would take control of the Nazi Government.

Well he premptivly sent a telegram saying he was declaring himself the new Fuhrer. Hitler saw this and went in to a rage. Hey battles over head, he had bigger problems to worry about than his former best friend forever freaking out in Southern Germany. So Hitler stripped Goering of all titles, ranks, medals. Everything and had him arrested by the SS.

Goering did not die by Nazi hands, and was eventually captured. But because of his political blunder, even at the bitter end, cost him his career and power, and in turn Admiral Karl Doenitz was given Presidency of Nazi Germany and ran it from Flensburg in Northern Germany, for up to two weeks after the war ended.

So if the show is anything like that, politically, yes 100%.