It does contribute, but the contributions are not always for the good. Because of globalization, different countries have different standards for what they think sustainable prosperity is. In a poor country, their standard is much lower compared to ours. We want everything readily available to us and globalization has allowed that to happen while it has also let other countries suffer.
Globalization contributes a lot to sustainable prosperity. With trading which is a way of globalization it helps sustainable prosperity because sustainable prosperity means meeting the needs and more of everyone for generations. By trading everyone is meeting their needs and helping each other do it.