There will be some challenges, in my view:
1) Wood is quite a good insulator (air in dried cell walls); all of your cooling will have to be convective (air)
No problem there -- most PCs are air-cooled anyway. I don't see any reason why liquid cooling wouldn't work, if it doesn't leak and care is taken to prevent excessive condensation. IMHO wood's insulating property is a non-issue.
2) It will be harder to make significant venting while keeping rigidity; a hardwood would help.
There's no need to make the case "just like stamped metal, but wood". In other words, don't even try to emulate stamped grilles. A wooden case could have a nice big air inlet in the front, facing down if the large hole doesn't look right. In the back, who cares?
3) Is there any advantage to the mount being a ground for PCI/AGP cards & Mobo? (if nothing else, to minimize static buildup)... if so, you might consider using a slide-out motherboard tray from some standard case.
I've had nothing but trouble from conductive mounting points. Once I even had to go to the trouble of taping every exposed metal part of the case that came in contact with expansion cards, just to get the thing to boot. I'd say that this is one place where wood would be better!
OTOH there's the matter of electromagnetic compatibility. Computer parts radiate a lot of RF energy, and can wreak havoc with radios and TVs if not properly shielded. The easiest way to do this is by encasing the parts in metal. But there are sprays that can be applied to cut down the interference.
You are false data.