The initial landing would have been successful, assuming German air superiority and an actual will to execute it, of course. There's simply not enough time for the Royal Navy to interrupt the landing unless they're already assembled so close to the beachhead that they'd risk getting taken out before D-Day by the Luftwaffe. Also, the landing would have involved plenty of paratrooper and airborne infantry as a first wave.

The big question would have been resupply. Germany didn't have the mulberry harbors and thus would have been forced to capture a port and ferry supply and reinforcements through it. That's when the Royal Navy could have run interference and I have no idea how that would have turned out.

So in the end, I think that the Royal Airforce saved the island.