They are actually more efficient also, as the wood doesn't need to be dried or cured before being used. That is why the Germans started using them, since they simply didn't have the 2-3 years to properly age the walnut while engaged in a full-scale war.
The original lumber would still need to be dried either before or after it was cut into veneer but certainly before it was laminated. If it were cut into veneer first it would shorten the drying time, but not eliminate it. I think any time saved would be offset by the time required to do the actual laminating. Surely the Germans, and the Soviets for that matter, were using a kiln to dry their stock material rather than waiting 2-3 years. Otherwise how would Izhevsk have produced over a million M91/30s within a couple of years of the war starting?