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.
Edit to say, I’m pretty sure any surge protector worth itself has a ground output on it already. Just run a wire from it into the literal ground if possible, or over to a place in your home that is properly grounded. You’re just trying to give something like a lightning strike a path of least resistance to discharge into. Any metal conduit in your home SHOULD be grounded, so that’s an easy option.
