I suspect, given the history of aircraft v surface vessels, that the German's could have managed it without total air superiority - they'd have lost a lot of men but once they got onshore I think it would have been only one result.
The history of aircraft v surface vessels showed that aircraft were very much the winners. I'm thinking of the Prince of wales and the Repulse, Bismarck, Taranto and Pearl Harbour. Also the Wehrmacht was built around Blitzkreig and they had zero experience with amphibious warfare. Although the British army was weakened they were the defenders and would have had the advantage. I think any invasion of England would have been equivalent to the raid on Dieppe. It certainly would not have been anywhere near the planning, equipment and resources that went into D-Day just for the Neptune component.
With the limited resources the Germans had for an amphibious assault air superiority was absolutely required to allow the Germans to support any forces that were able to land on English soil. The RAF and the RN would still have been strong enough to support the army even in its depleted state.