My experience is that silk takes the color better than wool does. I get very bright colors with silk vs the wool. I'm guessing you'll get three different, yet the same, colors. Each may take up the dye a bit differently. It'll be gorgeous, very unique! Be sure to share pics. I think dying blends is such a wonderful adventure!
You might want to shoot KP an email to ask them. It seems like they'd offer it as one of their dyeable yarns if it were dyeable. KWIM?
There is no right way to knit; there is no wrong way to knit. So if anybody kindly tells you that what you are doing is "wrong," don't take umbrage; they mean well. Smile submissively, and listen, keeping your disagreement on an entirely mental level. They may be right, in this particular case, and even if not, they may drop off pieces of information which will come in very handy if you file them away carefully in your brain for future reference. ~Elizabeth Zimmerman