Can I use this if "Region A > Shanghai" and "Shanghai > Region C" are separate flights?

When I'm searching for flights on Kayak.com, I'm looking for a 3-city trip. First is from Japan to Shanghai; next is from Shanghai to Taiwan; and finally is Taiwan back to Japan. But since Shanghai isn't a layover, I probably won't receive the Shanghai > Taiwan ticket when I check in in Japan. Can I receive the onward ticket (to be used six days later) when I arrive in Shanghai? Can I use the visa-free transit in this case?