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?
Additionally, without any ground wire to pull the housings of devices to ground, the potential for a short to energize the case and then electrocute you is also high.
this will also cause resets and instability. have seen it first hand.