Precisely. And not exploration for exploration´s sake, Henry the Navigator style. Mount Penglai holds the secret to eternal life - and not just that: Qin Shi Huangdi, the First Emperor, had been looking for Mount Penglai as well, or rather had sent people to look for it in his stead, so if the Yongle Emperor´s underlings found it, that would mean he succeeded at something that even Qin Shi Huangdi had failed at, i.e. a massive boost to his prestige as an Emperor. I´d say he´d go down in history as the great Emperor ever, but in fact he´d simply be the last Emperor ever, what with having gained eternal life and ruling China forever now.
You may have better luck with the attempted discovery of Fusang. If there are pessimists in the Emperor's court they are going to try to discourage this.
The fleets would still have to be able to sustain themselves over LONG voyages. And once it becomes clear that there are no real barbarian nations in the North/East beyond Japan, they´d either have to carry *everything* they need for the entire voyage, or the means to acquire it - they could even be expected to set up at least temporary bases to repair the ships and restock supplies. And from there it is a far smaller step to setting up a permanent colony if they have to than from the "handful of shipwrecked sailors in the middle of nowhere" scenario that seems to be the basis of the "not gonna happen ever" judgements here.
The OTL fleets consisted of hundreds of ships filled with soldiers, artisians, merchants, etcetc for showing Ming hegemony to the nations of South East Asia. Those are not going to be necessary for these voyage so there will be a more compact fleet, maybe a dozen, which is much more sustainable for long voyages into a mostly empty ocean across the Pacific. Once things get going we may see Treasure fleet ala Spanish gold convoys.
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That silver came mainly from two places: Zacatecas in Mexico, and Potosi in Bolivia; a Chinese expat presence in California might bring the former into its sphere of diplomatic/trade influence even without outright conquest, and a Mesoamerican power backed by the Chinese expats in California just *might* be able to hold onto Zacatecas against the Spanish.
What about discovery of the Inca?
San Francisco would be all well and fine for the location of an administrative capital for a full fledged colony but the region is just too well populated by natives for a starter settlement. Another place along the coastline would be better served as an interim colony before population concerns lead to looking for better places like San Francisco (and there is manpower to oust the locals).