Absolutely not.
The issue is the amount of current the AC cable is rated for vs. interconnects.
The AC ground is sized so that if a short to the chassis occurs it can safely blow the fuse/breaker in it or at the electrical panel.
The interconnects, and all the little printed circuit board traces are designed for nearly zero current. A ground fault with only the ICs for grounding is likely to start a fire at the IC cable, or melt it and leave the high voltage at the chassis.