Here in Chile and in Argentina, you can hear china with that meaning, but mostly in rural places by peasants. You'll never hear that from a person who live in the city. So, is quite possible that it's the case in Mexico too, I can't be completely sure tho. I know that it isn't the answer that you was looking for, but i hope it is useful to know that indeed that word can have that meaning in Spanish in some countries.

Aqui en Colombia hay algunas ciudades que lo usan.

Actually I would say in Colombia, I’m Colombian and we use it a lot

China is little girl in some parts of Colombia, I've heard it mostly in the capital Bogotá

No, China doesn’t mean little girl in Mexican Spanish. This word means female with curly hair