The chief consequence held was that the event of a man setting foot on the island would cancel the Amazons immortality and powers and end the way of life of which they had retired to on Paradise Island. These conditions were set by their patron and founder Aphrodite and formed a contract of sorts, one that combined with the Amazons longstanding wariness of man to virtually guarantee a place which would be forever apart from the world yet able to practice peace and learning over War and conflict.
One story in particular addresses the subject head on, Wonder Woman #216, and sees a story told that appears to be revealing the truth of the matter is that it isn't so much a literal apocalypse that would consume the island and Amazons but their society compelled to tear itself apart in lust over the man who sets foot on the island. Aphrodite's "cosmic Joke" as Queen Hippolyta puts it. It's not an explanation that makes complete sense if you think on it, and the story is possibly apocryphal given it was never referred to again, but the clever point to that tale is that a Legend is quite often more awesome than the mundane reality that lies beneath it...
Superman never then touched dowen upon their Island ever?
And could beings such as say Darkseid/Phantom Stranger/Spectre do that , as they are so powerful?