I'm sure Hitler would have had some interest in the Middle East to keep the oil coming. But of course, it all depends on exactly what kind of victory we're looking at. If you're envisioning the ASB total-victory that involves a successful Sea Lion, then the Germans will have a free hand in the Middle East without British or American involvement (total victory assumes Man in the High Castle victory, which would also have destroyed the USA).
Disaster at Dunkirk victory? Britain possibly came to the table, still has its empire, Germany has no direct impact on the Middle East.