I am going to give you an emphatic no, from personal knowledge.
In the town where I grew up and earned my first EMT credentials, Paris, KY, an off duty officer was killed by one.
Sgt. Fredrick fell down a short flight of stone steps when we had some late for the season ice. His cocked and locked .380 Colt Pocket was in a vertical shoulder holster as I recall and it hit the ground hard as he was falling and discharged. The bullet traversed his lower abdomen. A friend of mine was the EMT who picked him up, he was conscious, another close friend from those days was a fellow officer and was the investigator of record.
Clay survived the surgery and appeared to be recovering, but sepsis and a blood clot got him about a week after the incident. I have often wondered if he would have survived today because of better surgeons, better antibiotics, etc. etc. Or if he had been transferred to a better hospital in Lexington instead of the hack half ass small town hospital we had. There were no such things as trauma centers or real trauma surgeons in our part of the world in those days.
https://www.odmp.org/officer/5095-se...clay-frederick
Without a doubt the fall caused the discharge, I have no idea if the gun had been "worked on" or was factory stock, but there is little doubt the sear did not hold the hammer in that hard fall and tumble.