The whole civilization will not go down together, bits and pieces will survive and keep the faith.
But it will be a long dark night until the world reawakens again.
The world of the Renaissance was so vastly different from the height of the Roman empire, that they would have found few points of reference, if not for the islands of knowledge kept by the Roman Catholic Christian church in all the centuries in between. A lot was lost, but the rebirth was not from a world devoid of all knowledge of what had gone before.
Muslims, too, will become a forgotten and little-practiced figment of history insome future date, as quaint as the worship of Zeus and Thor.
Remember that the RCC saved western civ via the monesteries. They were able to preserve much from the Greeco/Roman times.