But the real thing isn't so much if China discovers the Americas--it has little apparent to offer they can't get elsewhere, and is full of random barbarians. But I think we all want China to colonise America, for the interesting effects of it.
I'm also interested in the effects on the American Indians. The French and English influence in Eastern North America in the early-mid 17th century created the Iroquois as a major force who triggered migrations of other people, and the creation of other very strong native groups. Combined with the Spanish pushing up from Mexico, they reshaped North America.
If China, following either the route around Japan and Alaska, or miraculously discovering the Manila Galleon route and returning to tell the tale, finds North America (this will require China colonsing Oceania first), what next? Why should Chinese go there? How can we get thousands of Chinese to go to the West Coast of North America and start settlements? Gold and silver is not a trade good initially, since the California Indians at least didn't know of it. Furs don't seem too important, since there's always North Asia to get them from. I guess if Chinese traditional medicine or others gives value to certain New World animals or plants, you could something valuable out of that. So it seems hard to get China to colonise the place. The Chinese would be more likely to settle in Mesoamerican civilizations or the Andes as merchants and amongst the most "civilized" people of the Americas, rather than striking it out in the wilderness of California or the Pacific Northwest.
Introducing horses into North America is one thing Eurasians are good for. China will be doing this. Meaning different groups of American Indians will get the horse through trading, and different groups of people will dominate the Great Plains. I could imagine the Chinese ending up giving Numic-speaking groups the horse, the same groups which become the Comanche, and then we still have the Comanche dominating on the Plains, although without the Spanish, their history will of course be different. Who else might benefit? Maybe the Cayuse, the Kootenai, other Shoshone, or some other group--it would be cool for some California native group to end up evolving into a dangerous Great Plains empire thanks to Chinese influence.
The Chinese would cluster around the harbours on the California coast. The Central Valley is very rich for agriculture, but is prone to disastrous floods, as in the 1860s. And there were worse floods in that region in the 2nd millennium, which is expected, since its basically a branch of the Pacific Ocean which dried out. An early Chinese colonisation would mean they might be exposed to be a terrible disaster.
And speaking of disasters, there's the 1700 Cascadia earthquake, if the Chinese go for the Pacific Northwest. California had many major earthquakes in the early 2nd millennium as well, and I find it disappointing there isn't a good list of prehistoric earthquakes (the info is scattered everywhere), although geologists can determine major events. There's also the whole decades long drought, which occurred in California as it did in the rest of North America
But if the Chinese stick it out, they'll find a productive, useful land, which will soon produce precious metals, as well as facilitate trade with Europeans on the Great Plains.