I highly doubt it.

I once tried to fly on that white piece of paper that the PSB issues when it is holding one's passport, and I got about as far as the check-in counter in BJ Capital Airport and was refused and escorted out.  Humiliated to say the least.

With the current restrictions in place, I would say no.

You might be able to purchase a train ticket but since they have started to verify ID cards and passports on trains, that might not be possible either.

For chinese people, they can get a temporary photo ID for civil aviation only, at the airport. But im not sure for you. You can call your carrier or the airport.

I did fly in September with the PSB paper they issue while holding your passport for visa renewal. When you get it you need to specify that you will need to fly, and they will send you to a counter to chop it.

Did fly Guangzhou to Shanghai and back.

My friend also flied with that paper. But it was a fight in one province - from guilin to nanning. 

Please get others transport mode like bus or private car. To avoid the unneccesary problems. If no others choice,you need to face the risk with others travel document.

I am curently without my passport as well while the residence permit is processed. I was told by the PSB officer who handled my application that the receipt for the pasport would enable me to travel anywhere in China.