Apply for South America Visa

I am a citizen of India and I currently reside in China on a F visa, my employer has already applied for my Z visa and it is under process. My employer would now like me to go on a business trip to South America so my question is will the embassy's/consulates here in China allow me to apply for a visa as I don't hold a Z visa for China yet?

Are there any other options? I will be visiting most all countries in South America.