72h/144h Visa-Free Transit

I am having the following situation and would like to know if I am allowed to use the 72h/144h Visa-Free Transit in Shanghai:
I studied Chinese in Shanghai and I am leaving from Shanghai to Taiwan because my student visa ends. In Taiwan I will stay 9 nights.
Then I want to travel from Taiwan via Shanghai to somewhere else (i.e. Japan, USA, Europe). Is it possible for me to use the 72h/144h visa free transit in Shanghai?