I know that the answer is yes, I should, but outlets near the setup are not grounded (even though they look like they are) and I don’t want to have wires running though my living room.
The real question is what are potential problems ? Occasional system reboots? Permanent damage to PSU? Permanent damage to other components?
Heh. House I rented was built before ubiquitous electricity. At some point, someone slapped a fuse box on the outside of the back wall and drilled a bunch of 1" holes in said wall to pass wiring. House was built on piers, so they just dragged wires around to places where they wanted outlets, which were mostly planted in the floor. Not a ground wire on site. I have no idea how they got away with renting that out, but it’s not like I called code enforcement, either.
My house was built in 1939. Initial installation of ecectric cables consisted of a wire in a sleeve filled over with concrete. That was all replaced with proper tubing and isolation, but these few outlets do not have ground.