If you are thinking of trying leather dyes l think Id want to do serious testing on scrap timber first to ensure whatever you put on top is compatible.
As long as the leather dyes are water or alcohol based, there's no compatibility issues that I'm aware of. (providing they are thoroughly dry before applying the top coat) The Angelus Leather Dye I have used is alcohol based and I've had no problem with Tru Oil, Polyurethane or Acrylic Lacquer.

Will the leather dye also work on necks?
As long as the neck is made of wood, yes!
However, the type of timber can effect how well a dye (or stain) works. For example mahogany takes dye/stain differently than maple because it's a much more open pore timber, but Maple can absolutely be dyed. It just doesn't suck it up as much as hog and can be more susceptible to blotching.