I want to come to Shanghai in february. will I be able to enjoy the free 72 hours policy?

If I bought a ticket into Shanghai, but had another flight ticket to leave the same airport to go to Taipai (Non-layover) during the 72 hours can I still enjoy the policy? I wanted to visit a friend in Shanghai and I want to know if I can stay the whole 72 hours with her or will I have to buy a visa :/