Red: The RN without air cover isn't staying in the Channel for long. WW2 is rife with examples of what happens to surface warships that face hostile air power without cover.
No.
First, not all hostile air power is created equal. When the Repulse and the Prince of Wales were sunk, they were sunk by a hostile air power that was specifically trained and equipped to do that. The Luftwaffe wasn't that air power in 1940. It might become that air power given enough time to prepare - which will give enough time to the British for countermeasures.
Also note that the Prince of Wales or the Yamato were sunk, the air power had complete air supermacy - not just air superiority. To get that over the Channel, one has to erase Fighter Command first.
Second, the Royal Navy will stay in the Channel for as long as it takes. Assuming it will take 100% casualties, it will do that. That's the reason of its existence, preventing blokes like Napoleon to come over uninvited, by sea. It will not try to save its warships if that means letting the Germans roam through Kent.
Third, assuming such a down-to-100% race, and assuming reasonable loss rates on
both sides, the Germans run out of Stukas before the British run out of destroyers. It's as simple as that. Check the numbers. The Germans, given an early enough POD, may have more Stukas. The British (and the rest of Europe) will notice that early on, too.
Fourth, there are no Stukas or Bf 109s over the Channel at night. Nor in bad weather. But if the German invasion force has to be supplied, there are convoys. And there will be the Royal Navy. Which is trained and equipped to fight at night. Heck, they only have to steam by a barge convoy to sunk it in their wake. There is no amount of PODing that will change that, barring ASBs that provide the Luftwaffe with some 10 years of technological head start for all-weather anti-shipping operations.
Fifth, assuming the Germans magically manage to run convoys only in daylight and in good weather, they still need the ports to unload. The Royal Navy can move at dusk, reach Dover, bomb the port facilities to nothingness around midnight for a couple of hours, then be out of Stuka range by dawn. Again, given years from the POD, the Germans may build a super-Stuka with a longer range - and again the other powers will notice that. Besides, if that super-Stuka attacks the Royal Navy far away from the Channel, it will have outranged the historical Bf 109, so it can be slaughtered even by Blenheims. Again, you can also give the Luftwaffe super-109s, so that they have the range to escort the Stukas far up the North Sea. And, again, somebody will notice that early on.