Though the 'Little Ships' were brave and rescued many, most of those evacuated were by Destroyers and other Naval vessels such as Minesweepers, they suffered heavy losses doing it and the civil vessels became more important once the port facilities had been flattened.
I've never brought into this 'Operation Sealion' either, nor did much of the German High Command. The Navy knew it had no amphibious vessels, (so river barges were converted to be be towed across at night, max speed 2 knots and no swell).
While modern, their Navy was small compared to the RN's and had taken losses in Norway they had yet to recover from, so escorts would have been an issue.
No doubt Goering would have claimed his Luftwaffe would destroy any British fleet powering down to destroy any invasion force but they had failed to do this at Dunkirk, under for them, much more favorable conditions. (The first time Spitfires were used in any numbers was covering the evacuation, German air losses were rather heavy so despite the impression many on the beaches had of the RAF not being there, they were, further inland interdicting the air attacks, at least by enough to prevent Goering actually delivering on his promise).
It does seem likely that the Panzers halted as Goering promised Hitler that his Luftwaffe could alone finish the job. Hitler was prone to take his dubious advice because unlike the army, the Luftwaffe was something created under his regime so in his mind, loyal. None of those Prussian Officer Class types at the top of the army, who he never really trusted, despite the victories they gave him.
While it's true that the BEF left most of it's equipment behind, that was in late May/early June, by September the situation was rather different. The UK had organised war production much more effectively than Germany, not only that, an array of defences on beaches and inland were ready, even the Home Guard had weapons by then!
The Germany Army and Navy could not agree on an invasion plan, Hitler was not about to force the issue. Some reckon this was because he was already thinking of going East, which might well be the case but more likely he saw the Luftwaffe gaining air supremacy over at least Southern England, coupled with the U-Boat campaign, as a way of getting Britain to sue for peace, forcing Churchill from office.
Despite the real damage done on air defence targets, only one airfield, in Essex, was put out of action for more than a few days, likewise radar stations were usually soon repaired and there was a degree of overlapping coverage.
None of this means the Battle Of Britain was not vital, just that the invasion plans were not realistic, even if 11 Group had been taken out of the fight, 12 Group normally covering the midlands, still was.
Invasion or not, the strategic intention was still the same, to get Britain out of the war. That was something they might well have managed to do, the RAF stopped them.
In that, the Luftwaffe failed, Goering's inept leadership being a factor.