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?
You food should expire that quickly. It would take at least a day or two.
Unless your gone for a while you would notice that the lights no longer on and it doesn’t feel as cold.