Now that I've got my book in hand - the entry for Training Lightsaber states it does have a crystal, either a kathracite or danite crystal. They also have a low power output generator. To turn it into a full-powered lightsaber one needs to replace the crystal and the power generator.
I thought all that was needed was to insert a crystal.
This entry also refers to the training emitter as a crystal. And the emitter entry explicitly says it's a lightsaber crystal so fluff wise it's a kathracite or danite crystal but mechanically it's a training emitter.
Edited by Jedi Ronin