The rational for constrained layer damping is that the product absorbs vibration and converts it to heat---not reflecting the mechanical energy back to it’s source, but instead dissipating it. That’s the theory, anyway. I really doubt damping tape can prevent an arm tube from vibrating! It CAN absorb vibration though, and is in fact designed and intended to do just that.
EAR damping products are widely used in commercial applications, to reduce the level of noise produced by large machines in manufacturing plants. In music systems, constrained layer damping (used in some of the world’s best loudspeakers, and in some isolation platforms, such as those made by Symposium Acoustics) can be used not only on tone arms, but also the metal chassis’ of electronics, many of which ring like a bell. That doesn’t necessarily mean the sound of those electronics will be improved, but it’s cheap to give it a try and find out.