Yes, it's been done... and then some.
As far as gluing a layer of carbon fibre on top of a wood body, you probably wouldn't have much of a problem, other than the fact that it's a) a hell of a lot of work; and b) it will likely be permanent.
As far as i know, you have to use epoxy adhesives for attaching carbon fibre to anything. Forget about ever removing it. You'll have to do a lot of sanding to get it smooth, and likely will have to use marine epoxy gel coat to get a smooth, clear finish. Lots more sanding. But it will look SUPER cool.
Mind you, i've never done this, so i'm just guessing. You can probably find out a lot more about carbon fibre out there on the Interweb... loads of hobbyists are using it for boats, automotive parts, bikes, etc.
As long as you don't have the carbon fibre come in contact with anything that's carrying a live signal, you shouldn't have any problems at all with its conductivity. If anything, it'll give you some pretty kick-ass shielding if you wire it to ground. (If you leave some bare fabric in the holes where your volume and tone pots go, it may make enough contact to be grounded that way.)