No doubt that Hitler may take Africa and the Middle East.
The bigger question is whether or not he can keep them? His supply lines will be stretched. The British navy can also set up shop, new bases wherever and whenever they want to deter the Germans.
Add to this the Nazi ability to make enemies out of conquered peoples once the SS comes along.
He would have to have some amasing luck to be able to keep his possessions.
If Spain, Vichy France, Turkey joined as junior allies, while liberating Syria and at least putting up a puppet in Iraq to control the people while Germany controls the oil.
If he could avoid direct confontation with the USA. Once the weight of the USA is added to the British, he is screwed no matter what he does.
What would he do after he captures North Africa and the Middle East? Would he make a move towards India? Would he prepare for the Soviet Union? Would he step up the air and naval campaign against the UK and wait for a British counter attack?