isn't a lunchbox locked all the time and clicks/skips over? in that case what difference does it make if you have power going to the front or not, still dragging one wheel and slowing the other and will skip as you go, the steering will fight you and won't be smooth like an open diff - at least that's what i understand the issue is up front, in the rear is not as obvious since you're not steering it.
When I had the D30 with a Detroit, in 2wd you could not tell it was there at all so I would assume the lunchbox lockers would be invisible too. When I ran a Lock-right in the rear it was very noisy around corners until I learned how to minimize it. (Detroits are way less noisy)
When the lunchbox lockers lock and unlock they will ratchet with the spring set up they have. But in 2wd this should not happen, it needs torque from being in 4wd to make it ratchet.
I think you are right and they are locked all the time and when they unlock around corners is when you hear them. With a locker with springs (lunch box or Detroit) when cornering either the tire will slip on loose/wet type surfaces and you won't have locker noise because the tire has slipped on the road/trail surface. If the tire can't slip then the locker will unlock to allow better cornering, that's when you hear the noise or feel it though the suspension/chassis.
If he is getting issues in 2wd I would say something is not right in there. I don't know what it could be but there should not be any issues in 2wd.