No. It’s almost certain to violate your local electrical code. It is to ensure that circuit breakers trips when they have to. Grounding your electrical system to more than one location can cause breakers not to trip during a fault.
Earth (isolated) ground vs. wall outlet ground.
Looking on my 200amp main panel I notice that the neutral (white) wire bus and the ground (bare copper) bus have continuity. Wouldn’t it be better if my interconnected rig had it’s own earth ground thereby isolating it from feedback from the neutral wires? If not (NEC rules, Ott’s Grounding Myths, etc.) why is there a ground lug on some of my pieces? Surely it’s not there for decoration. I can’t imagine a manufacturer adding a useless item (adding cost) in a hidden place if it didn’t have specific function. All my pieces are connected by balanced XLRs (except the speakers) and the balanced XLR has unified grounds. Inquiring (and in my case sometimes simple) minds what to know.....