Yes! I think training in this area is critical for any organization running Holacracy. Without training on GTD methodology, you'll have trouble getting people to effectively leverage the system and maintain productivity as they transition to self-management. We have a couple of roles responsible for carrying out this kind of training.
Unlike one of the commenters above, we do not require any particular software/tool be used for trusted systems, only that each person have a reliable one. It comes up from time to time that perhaps by policy we should restrict to 1-3 tools so that we can drive greater alignment between people and get more detailed in our trainings, but we haven't taken that step yet.