Does wood filament damage the printer nozzle?
If you haven't been to their site before, you should check out the forums on 3DHubs. There's a lot of how-to's. A quick Google search yields this link to a similar question.

The key thing to note is that in all technicalities, any material you run through the nozzle is going to cause some sort of wear on your nozzle. How quickly depends on the material or composition.

The answer to the question linked above relates it spot on to sandpaper. If you have sandpaper made out of metal (ie stainless pla), it will scratch your skin fairly easily. If you have sandpaper made out of tree bark (ie laywood pla), it probably won't scratch your skin as bad, but it'll still scratch. And just for poops and giggles, lets say you have sandpaper made out of pla; it'll take a while, but you could eventually make your skin raw if you rub the plastic against your arm long enough.

It is typically recommended to use one nozzle for each material type as to avoid cross-contamination of materials in your printing. With this idea in mind, if you are using many types of materials, you can also minimize failed prints due to clogging and other "damaged nozzle" type troubles.