I just don't think it will do anything for the appearance of the damascus other than make it dark and add some swirly colors at best.
Simple acid etching is what gives modern Damascus steel its dark/silver contrast in color. Acid etching and hot bluing would give him the visible color variation only darker. Both processes are less likely to negatively effect the temper of the metal because they don't involve heating to 1300F for 6 hours like case hardening does.
But I am going to stop because I think i am right, and so do you. But if you go to google and search for color case hardening Damascus you will find this conversation at the top of the list... Other than that it looks like most people agree that damascus steel should be acid etched or hot blued if you want to change its appearance.