Well sort of.........well sort of.
There is a difference between the locker disengaging and it locking up......slightly different functions, I mean. It will lock up when torque is applied, but not necessarily disengage when torque is not applied. It will disengage when turning, but not necessarily if torque is also applied. It will stay locked if you are going straight even if coasting (no power applied), and it can disengage when turning even if some power is applied.
The locker works by becoming a spool under power (locking up) and differentiating around corners (disengaging). Torque from the driveline will lock it up, but torque from the axle will disengage it. The locker disengages (differentiates) when an axle spins ahead of the carrier, so an axle can spin faster than the carrier, but not slower. What happens in a turn is that the outside tire spins ahead (locker disengages) and all the power goes to the inside tire. If power is applied smoothly and moderately you won't feel anything. If you give it enough power, and are in a tight turn, most likely taking off from a stop making a right hand turn, the inside tire will spin and chirp. This is caused both by the inside tire getting all the power and the weight transfering in the turn to the outside tire, letting the inside tire break loose. The chirp, chirp, chirp is from the inside tire catching up to the outside tire that was spinning ahead, then the outside tire spins ahead again and the inside tire breaks loose and catches up again, and again. If enough power is applied to lock up the locker, either the inside tire will just spin and howl (not chirp, chirp) or both tires will break loose.
The kick that is felt in the rear end when turning and shifting or when turning back and forth, like driving on a tight mountain road, is from the locker alternately switching sides as the inside tire switches from side to side. What you feel is one axle powering the rig, and that one axle is switching sides every time you change directions (inside axle always stays hooked up while outside axle spins ahead). Now, if you turn back and forth AND let on and off the gas, there are multiple switches in sides with the power from both the turns and accelerating and decelerating. The unique driving characteristics of an automatic locker actually come from it disengaging one side (differentiating) rather than from it locking up.
As far as when it will lock and when it will disengage, it depends on the traction and the power applied. If the torque appied from the faster spinning outside tire is more than from the driveline, it will disengage. If the torque from the driveline is more, then it will lock up. You can think of a locker as your ratcheting wrench and a socket. If you pull on the ratchet handle, the socket has to turn, but you can grab the socket and spin it ahead of the ratchet.......just like an automatic locker.
The annoying chattering of a lunchbox locker when making tight slow turns, like in a parking lot, is from there being slack in the drivetrain, and the locker can't decide which side to engage. If the smallest amount of power is applied in this situation it won't chatter, the inside will lock up and the outside spin free like it is supposed to. This tendancy is much greater in a stick than in an automatic, since the auto tends to keep more pressure on the drivetrain. The reason this tendancy doesn't happen in a full Detroit is because the side gear rides up on ramps when differentiating and so the gears are fully seperated while differentiating, while in a luchbox locker the side gear rides up and down on the bevel of the dog teeth while differentiating.
Hope this helps some have a better understanding of what makes a locker work.