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?
Looks like your landlord and the people who flipped my house hired the same electrician. They did the same stupid thing jumping the load and ground so that it’d pass inspection (the little tester will show everything properly grounded).
Unnnnfortunately, that’s also a good way to cause serious damage to things and in my case it managed to short in such a way that it melted one of the phases coming into the house and damn near burned my house down.
Don’t do stupid shit with your outlets, kids, because uh, yeah, fire.