It's been done, but final looks depend on your skill. Gluing it together might be easier, but it will probably look better when using more advanced technique.
Wood can crack and change shape as it dries, so make sure wood you use is completely dry already.
Other than that it's even safer than having metal case, because dry wood doesn't conduct electricity, even if some exposed parts touch the case it shouldn't short anything out...
Probably the one to look at:
Too advanced: