As I said, I don't have a P3 to test but you could easily try it with yours if the motors will still spin up. Place the prop on loosely and spin up the motor. Shut it down and see how difficult it is to remove. That should answer your question.
I get somewhat frustrated and the folks on here who jump on anyone who reports a crash and tries every way possible to convince them that it was their fault. DJI has had a history of flyaways, bad solder joints and power failures. I would like to believe that the naysayers are just fanboys who can't admit that their favorite toy could have defects, but their behavior is so rabid, that I wonder if they are paid by DJI to troll these forums and discourage new folks from reporting failures.
Don't let them get you down. Report your problem and hope that DJI does the right thing.