Relatively recent fossils, in which the original calcium carbonate ground substance is still present, would still be susceptible to Byne's Disease. It would probably be more difficult to detect visually in the early stages, since the surfaces of many such fossils are already somewhat roughened, eroded, chalky, etc., and much of the original pigmentation is gone. But there is no reason why such specimens should be immune. It is still the same chemical compound, so exposed to the same chemicals under the same conditions, it should still react the same. Older fossils, in which the original ground substance has been replaced by harder, non-carbonate minerals, (especially non-calcific non-carbonate minerals), would probably not be susceptible to this kind of chemical decomposition. Materials can easily be tested for susceptibility to Byne's, if you have a small piece of a specimen that you don't mind sacrificing. Just drop the piece of material into any acidic solution. If you see bubbles rising from the piece of material, you are seeing the same reaction that occurs in Byne's Disease, only in accelerated form. If you use a very weak acid, like vinegar, the rising bubbles will be very fine and not as obvious, but can still be seen by close observation. If you use a stronger acid solution (something like 10% muriatic acid), the bubble production will be immediately obvious. If you use a very strong acid (like 100% muriatic acid), and a substantial piece of shell, the bubble production may be so violent as to cause the acid solution to splash out of the container, so that is not recommended.