I have a single entry China visa, can I still take advantage of the free transit for one entry?

My routing is YVR - Shanghai (for less than 72 hours) - Hong Kong, then returnt o Shanghai (this time will stay for a week), and then back to YVR.

I only have one single entry. The question is can I take advantage of the 72 hour free for the first stay in Shanghai? Will they give the permit to me, even when I already had a single entry one in the passport - but I want to use it for the next entry into Shanghai.