Travelling from TAIPEI via SHANGHAI to LOS ANGELES

HI!

I read in your post that if you travel via TAIWAN/HK/MACAU you can't apply for 72 hours visa. I will be living in Taiwan for 4 months and want to go back to LA via Shanghai with a stopover of 16 hours to do some sightseeing and visit friends. So technically my flight leaves from TAIWAN, via Shanghai to LA... can i still enjoy this free transit?
Do i have to take out my luggage and then check in again?