I thought this 'new' idea had been accepted for a while. The LW alone could never have done enough to allow the Germans to launch an invasion in 1940. The only tactic they had that began to work was the effect of attacking the airfields themselves - and even had that been 100% effective the RAF would simply have moved its squadrons north, out of the 109's range, and operated from there.
The German army never had anything like the support it needed from a navy that had just got a severe kicking in Norway. Putting thousands of troops on barges used to trading on the canals of europe (many unpowered) would have been catastrophic. All the RN would have needed was one warship to get in amongst them and the crack invasion troops, who incidentally had, er, no amphibious training above river crossing) would have been destroyed. Remember, even in a relatively long campaign like Crete the Navy managed to keep the majority of its ships afloat. In a german invasion the ships would only need to make one, possibly suicidal, sortie. The LW didnt even have a stock of anti-capital-ship AP bombs.
They had no plan for resupply once the troops were ashore, and no bomber force capable of a long term strategic campaign - the RAF and USAAF didn't win the war even with 100 times the destructive power of the LW.
You will find no greater admirer of the Few than me. However, 'failure' in Aug/Sep (a retreat to Leicestershire by the RAF, the South coast towns more heavily bombed than before - neither exactly a war loser) would not have led to an invasion. What success did do however (and they did succeed in stopping the LW daylight bombing campaign) was immeasurable in both morale at home, and support from abroad.