Why overwhelming bombers still would not make Sea Lion work

If the Luftwaffe received twenty TIE bombers, could Germany carry out Operation Sea Lion?

No; the bombers could devastate Britain, but Germany would still lack the amphibious shipping, infrastructure, and sustainment required for an invasion.

Twenty Star Wars TIE bombers would give the Luftwaffe destructive power far beyond its historical aircraft. They could reduce British targets to ruins and transform the air campaign. That does not create the barges, trained amphibious forces, escorts, ports, and resupply system needed to put an army ashore and keep it fighting. The scenario isolates a durable strategic lesson: bombardment can devastate an opponent without solving the logistics of conquest.