Garrett Hardin, the famed ecologist, would probably be in favor of the concept of global citizenship. This can be inferred from his famous paper "The Tragedy of the Commons," in which he postulated the idea that a group of individuals, each acting in their own rational self-interest, would necessarily damage a shared environment or resource without malice (Wikipedia). Hardin also claimed that increased government regulation would be useful in halting this damage. Through this view, it can be inferred that global citizenship, in which all people share a common nationality (The Earth) and are equally responsible for its care, would help to limit or halt the destruction of global resources.
Hardin's view takes into account the idea that an individual's rational self-interest is not necessarily a positive influence on others, regardless of intent or result. The overuse of resources without a limiting factor (such as a government committee) almost always leads to the destruction of the resource in question, even if steps are taken to repair the damage. For example, a logging company that cuts down every tree in a forest damages the local ecology and removes the positive envionmental aspects of the trees; if that company reseeds the land, it will take years before the previous positives of that forest return.
Under Hardin's (hypothetical) approval of a global citizenship model, all citizens would have the knowledge and the personal responsibility to act in their self-interest without damaging overall resources. A government body that oversees activity on an individual level would limit and enforce these laws, and cultural opinion would shift to support a collective world culture, rather than an individual one.