Would this cause any damage?
I am not an electrical engineer, just a tinkerer, so I'll leave it to the experts.
I am an electrical engineer, and I think it makes no sense.
With a fully balanced amp, it very likely would cause damage, because since both the + (red) and - (black) outputs of the amp are actively driven, you would be grounding an actively driven output.
For the same reason, you would probably also cause damage in the case of an amp that is operated in bridged mono mode. And also in the case of an amp operated in stereo mode but where the amp is one of those few amp designs that on one channel have the red terminal grounded and the black terminal actively driven, to facilitate bridged mono operation.
With amps that, like most amps, do not fit into any of those categories, you would not cause damage but there is an excellent likelihood that you will degrade the sound by introducing a ground loop. I can conceive of no circumstances in which doing what you are proposing would provide a benefit.
Regards,
-- Al