If a Drill's Clutch doesn't properly align the gears, can it cause the Chuck to loosen?
That was a close one! I would surmise from your description ("The drill's chuck isn't keyless, or at least I haven't tightened it without the key") is the cause of the spitting drill chuck. I too am guilty of being in a hurry and trying to save every second and bypass the chuck wrench. The other issue may have been caused if your drill has a High and a Low speed setting. If the lever is placed in between the two speeds the gears (as you have mentioned) may not mesh. The resulting grinding sound is not a pleasant one. I've had a similar scenario using a DeWalt 18V Cordless Hammer drill.