My new darkside bike is full carbon and I'm wondering if I need to put some helicopter tape around the headtube where the cables are touching?

It surely depends on how dirty it's going to be? I wore a hole in a previous alloy frame with a nylon tie-wrap. It wasn't the tie-wrap at fault, but the grit beneath it.

Yes in a word.
As mountaincarrot said you can wear a hole in aluminium,(the side of my head tube has 1.5mm deep grooves in it from un protected cables and riding in Peak District grinding paste) I'm sure the epoxy that holds the carbon together isn't much harder than aluminium and the consequences of it to a carbon frame are much higher. If you don't want to use heli tape, Park instant puncture patches on the frame do the trick and are cheap.