Whenever this topic comes up, I always want to ask people "go, look at a map." The Pacific is HUGE. Much bigger than the Atlantic. Seriously, it's not even close.
And while the South Pacific has tons of little islands (none of which would be worth the time of any Chinese emperor), they trail off to empty ocean well before you get close to America. Hawaii, in particular, is isolated, and generally useless before the introduction of steamships.
Note that it took decades for the Spanish, after the success of Magellan's expedition, to discover a repeatable route for reliably crossing the Pacific, and even that was extremely dangerous. That was with strong motivation (the Spanish knew that China and the Spice Islands were on the other side), here your hypothetical Chinese will need to be willing to make these dangerous expeditions without knowing that there's anything of interest on the other side).
That's without getting into discussions of currents, winds, Chinese culture, technological capabilities of the ships, etc.