Actually, you're worrying in the wrong direction. The PSU gets its connection to real Ground via the power cord. But how does the rest of your case get grounded? Two ways:
1. via the contact and screws where the PSU is fastened to the case, and this may be disrupted by your painting plans. However, AFTER painting you could ensure that at one spot somewhere - maybe inside where it's not visible - you crape away a bit of paint and install a bolt securely-fastened through a hole and making good electrical contact. Then install a jumper wire from that to one of the mounting points on the PSU case, thus ensuring the ground connection originally intended.
2. via the mobo itself. Several connection cables between the PSU and the mobo contain Ground connections. SOME of the Ground points in the mobo also connect to the case at the mounting points where screws through the mobo connect to mounting standoffs. IF these are metal standoffs that are securely screwed into threaded holes in the case itself, that establishes a Ground path from PSU through mobo and standoffs to the case metal. HOWEVER, this is not a really good ground connection suitable for significant currents, although it will help with reducing the small currents involved in electrical noise.