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?
Other question for anyone listening here: How can we check if an outlet is correctly grounded ? I live in a faily new appartment with good outlets, but maybe I should make sure they are OK ?
$10-15 will get you an outlet tester at just about every home improvement store. You plug it in and the three big LEDs light up and you compare it with the sticker on the device. Get one with a GFCI tester built in, when you press the button it will short to ground and if your receptacle has GFCI protection or is on a GFCI protected circuit should trip the GFCI protection.
Something like this
https://www.amazon.com/Receptacle-Tester-Klein-Tools-RT110/dp/B01AKX3AYE/
or this
https://www.amazon.com/Receptacle-Tester-Klein-Tools-RT210/dp/B01AKX8L0M/
Grab something like this: https://www.amazon.ca/Gardner-Bender-GRT-3500-Standard-Outlet/dp/B000NBDTQI