Some run well ungrounded, and some just won't.
While it's true that the power supply plugin will ground it somewhat, remember that's not the greatest path.
Hoot's 5 volt mod article proves that...you have alot of power loss from the atx plug to the components, imagine what it's like once it returns all the way back.
Take a look once at the difference between bios voltages and what's read with a multimeter at the molex plugs...that's not imaginary (no I don't think it's terribly accurate, but it beats poking probes into a running board).
When I made my case, I made sure to include a copper sheet as a groundplane for all the motherboard standoffs to ground every single grounding lug on the motherboard (why do you think they are there, anyway?).
I'd suggest getting a piece of aluminum, copper, or steel sheeting to use as a ground plane, and hanging it by that. I'd also suggest using some fine cable called steel leaders from the fishing section to hang the mobo from. A loaded motherboard has some considerable weight to it, and the steel is also good protection against accidental snapping from bumping it with your noggin.
It's a skinny, multistranded cable with swivelling clasps to secure it well, and each will hold the full weight in case of an accident.
Oh, and where are my manners...
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