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?
Do you have money to replace everything plugged into those outlets, and sufficient home insurance that also ignores such things? Then, no, I guess.
Just take an hour and make a ground yourself. It doesn’t take a lot of specialized knowledge to do so.