Is Jarod Diamond successful in supporting his thesis in the book Guns, Germs, and Steel?

As it is an extremely large and complex work, there is really no single answer to this. Jarod Diamond's main answer to Yali's question of why Europeans have so much more "cargo" than the natives of Papua New Guinea is that it is due to geographical factors rather than innate intelligence or culture. The claim that differences in technological development are not the result of people in underdeveloped nations being somehow "inferior" is one that is widely accepted among educated people, nor was it the default belief when Diamond was writing; thus, it was not something really in need of proof. 
The cultural arguments are more problematic. On one hand, Diamond's arguments about the influence of the environment are quite interesting and, in my opinion, an important contributing factor. Complex human situations, though, can rarely be accounted for by a monolithic argument attributing complex phenomena to a single cause. Diamond has also been widely criticized for cherry-picking evidence and ignoring many significant cultural and historical phenomena. 
I would say that Diamond's work is an interesting and powerful argument concerning one of the potential causes of global inequality, but it is only a partial explanation. His work is well argued, using a wide range of evidence, but it is not perfect. It attempts to address such a wide range of phenomena and broad sweep of history that some of its explanations are superficial.