As most of us know it does not take the hammer to be cocked before a discharge can occur. Simply dropping the weapon onto a cockpit floor is enough to cause a discharge if you have "one up the spout".
A modern weapon in good working order, such as a CZ-75, Browning Hi-Power, Glock 17, Smith & Wesson 29 ("Dirty Harry Gun"), etc. will not go off if dropped even with one up the spout. The design of the gun makes this impossible, as the firing pin is physically blocked from making contact with the primer until the trigger is pulled. Some firearms, such as a CZ-75, are safe to carry even with one in the chamber and the hammer back, with the safety on
and the user is properly trained, especially with regard to holstering and drawing the weapon. On occasion, I would carry a CZ-75 in this condition.
Some older weapons (e.g. single action revolvers, original Colt 1911) can easily be made to discharge if dropped. A fault in a modern weapon can also render them liable to accidentally discharge if dropped.
I would hope that a pilot permitted to carry a loaded firearm onto an aircraft would be issued with a modern well designed firearm, and more importantly, be trained exactly how to handle the firearm safely. Alas, many "trained" firearms users that I've come into contact with scare the holy crap out of me with their unsafe gun handling.....
I'd be very interested to know exactly what type of firearm was being carried, and what the training requirements are....