A tow strap on the bucket is not going to hurt the bucket but it could damage the operator if the tow strap breaks and comes flying back at you. If I were to use the FEL to drag an object back while using a chain, (I would only use a chain and not a nylon strap due to the kinetic energy stored in the stretchy material ) I would keep the bucket on the ground in float position or at least very near the ground so any flying straps would be below the operator platform.
As for mechanical failure of the QA system, There is no issue there. It is stronger than any force that the tractor can produce. One does have to make sure that a limb or other object does not hang on the release handle and pull them up. If this happens, you can damage the FEL badly by springing one of the main beams when the bucket comes off one side.