Yes – like any clamp, this one can be damaged by over-tightening. This is especially true if the clamp is applied where only the outside edges of the jaws are contacting the object being clamped. In this type of application, over-tightening will cause the sliding jaw to bind on the shaft, and could even bend the shaft.
If you choose to apply the clamp in this way, use the minimum amount of pressure necessary to safely secure the clamp; and never use tools to tighten the clamp.