A locker or limited slip will always increase the torque on the axles. If the axles are locked together, all of the engine torque must be transfered directly to the axles. With an open differential, there is a torque split and there is often less than the total engine torque actually being transfered to the wheels.
Alot of Jeep owners abuse their stock axles for years without problems and then immediately break them as soon as a locker is added. Many odd driving situations that would not normally break an axle will be able to once the locker is added. That's especially true of someone who is accustomed to approach slippery conditions by stomping on the gas. Especially with the stock axle, you will need to be much more cautious and gentle when you accelerate after the locker is added. That's both to prevent breaking an axle as well as to prevent it from locking up and giving your car a slap in the butt around curves.
The good thing is that the axle shafts themselves don't normally break from torque, they break because of flex. A locker just increases the amount of torque the axle sees, and most shafts won't mind. The rigidity of the axle housing is important. The reason my family has had three Eagle axles break is because my brother and I were fond of jumping and tilting our Eagles on two wheels, which the thinner axle tubes could not handle. The center casting is actually identical to the Cherokee rear axle, but its called an AMC 15 because the tubes are thinner.