You're changing the terms of the debate. The question is not whether non-Western societies can "succeed," whatever that means, but whether Western civilization will survive.
Ideals don't create a civilization; people do. If Western people are overwhelmed by other peoples, the civilization that results will simply not be Western because because the people who run it won't be Westerners. It's that simple. The successor civilization might be economically prosperous, like Japan, but Western it will not be.
I disagree.
Our whiteness did not give us the Constitution. It was not the color of our skin that made America the first nation to have free elections. It was not our race that enabled America to survive, and prosper, with minimal interference from a central government.
It was the ideals, and the principles, EMBODIED IN THE PEOPLE who founded America which made this nation great.
If you think that our success was based on our race or the color of our skin, why are other caucasian countries [like in eastern Europe] so poor?