Last month I had to leave Chengdu to do some business and was in the similar situation as OP (visa extension in progress and no passport). PSB gave me a receipt after taking away my passport in order to extend my visa. Just the regular one they issue to everyone, nothing fancy. It had my photo, passport number, date of birth etc.
I called the airport and asked if they let me board the plane. They said that I more than welcome. I was able to fly into multiple places (Shanghai, Hangzhou some other smaller cities) without any problems at all. I also didn’t have any trouble to stay in hotels.
So if I could do it everyone else should as well.
Cheers