Skimmed through this. There is some excellent information in these comments, but I think a larger point is being missed.
The thread at this point is largely not about whether an industrial revolution would have helped (the consensus here seems to be that it would have) but whether the social environment of imperial China even allows for the possibility of an industrial revolution to take place. So far, it seems that the development of industry was possible, but it would require reforms to Chinese government that state-officials were unwilling to make at the time because it would disrupt the social system.
There's been a lot of argument about "the purpose of government", and based off what I've read here, I'm reasonably convinced that Chinese civilization followed a relatively different model of state development than the western one. The issue seems to be that the Chinese state slowly prioritized an idealized social system until the point where the institutions that kept the state afloat began to degrade, and then waffled on solving the issue because it would harm their already weak standing. I do think the silver would have helped at least kept the state afloat through institutional reform though.
It seems to amount to:
1) If our Althistorian can convince the Chinese bureaucracy to accept governance reform.
2) Would stabilizing the government make the bureaucracy more willing to implement changes in governance? ( I think so, at least)
The silver issue wraps around to the issue of "how do you prioritize and fund colonization, and ensure the government benefits?"
Although now that I think about it, i'm not even certain that the Chinese would need a colony in Peru, considering that the Indian Ocean trade was able to drain Rome gold and silver dry through goods and spices alone. I think that as long as you can trade with the Incans, and ensure their state against Europe, you don't even need to fund colonists to administer the natives in extracting the silver yourself, you can just do so by selling to their upper classes.