I wasn't actually aware of the amount of people it carried, thanks for brining this to my attention.
I'll just carry this matter on in private, I guess. /thread
Here is a summary with some additional links.
7 expeditions between 1405 and 1430. Up to 300+ ships with up to 28.000 crew members.
Large treasury ships, smaller war ships, transport ships (for horses for example), supply ships (with nurseries producing soybean sprouts) and water tankers.
The problem with "blown away to America" is prevailing wind directions.
You can see a simplified model here.
The ships couldn´t sail directly against the wind. So with a position in South East Asia or the Indian Ocean, they normally couldn´t have reached America.
In normal times they would have to sail North (Japan, Kuril islands) to catch a wind carrying them to Alaska.
Maybe with a strong El Nino event? Then the surface winds (Walker circulation) change direction (from West winds to East winds).
But even here you have the problem that the Chinese fleet on all expeditions traveled through the South China Sea and the Indian Ocean. Visiting Java, Sumatra, India, Arabian Peninsula and East Africa.
Do you see the problem?
Even if you now have winds blowing east your ships would probably first reach (depending on the location) the Philippines, Borneo, Celebes, New Guinea.
A ship would need to be exceptionally unlucky to miss all those "overlapping" islands. It´s almost impossible. And if it really happens then that ship wouldn´t have enough supplies for a Pacific crossing. So the crew either dies or reaches one of the smaller Pacific islands. And in that case why would they sail on? Even farther away from home?