From Kärntner Institut für Seenforschung (roughly translated, the Carinthian Institute for Lake Research) comes this poster on whether Marmorkrebs can spread the dreaded crayfish plague (click to enlarge):
The short answer is yes, as predicted. Although they can carry it, there are still no reports of Marmorkrebs in the wild carrying crayfish plague that I know of.
This poster was presented at the 16th International Conference on Diseases of Fish and Shellfish. This meeting had a large symposium on crayfish plague.
Kärntner Institut für Seenforschung
16th International Conference on Diseases of Fish and Shellfish