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?
Surge suppressors do not drop extra voltage to ground. They selectively short out surges between whatever two conductors have a high potential between them.
No ground conductor means there cannot be a high potential between it and anything else!