If the PSU has a power switch on it, yes turning it off (at the PSU) will work.
If the PSU doesn't have a power switch on it, then you want to unplug it. The PSU still sends power to the motherboard even when the computer is off. This is how things like always-on USB power ports stay powered even when the computer is off. How the GPU sends a signal to the monitor telling it to stay asleep, instead of the monitor displaying "no cable detected."
Given how expensive components like the CPU and RAM are, I just unplug every computer regardless of whether or not there's a switch on the PSU. It's just not worth the risk of frying something because you thought the computer was unpowered when it wasn't.
Grounding is not there to protect the computer from static. It's there to protect you from electrocution. Without grounding, if a short in the PSU electrifies something inside the computer with 110V AC power and you touch it, the electricity goes through your body to the ground, killing you. With grounding, the short goes through the ground wire, and blows the fuse or trips the circuit breaker, hopefully before you have a chance to touch anything that's electrified.
The metal chassis of the case is enough to absorb any static charge your body holds (edit: ok, maybe not if you've been playing around with a Van de Graaff generator). So it's good enough to just make sure you touch the metal case (or metal table leg, or some other large metal object) before messing around inside the computer.