No, a diesel engine works using compression ignition, i.e. there is no spark plug or electricity required for the actual ignition, it occurs spontaneously due to the very high compression of air and fuel in the cylinders. It's more to do with the Thielert's reliance on electronics than anything wrong with the engine itself.
Each engine has two electric Engine Control Units (ECUs). At least one must be working on each engine for that engine to operate. Normally if there is a major electrical failure in flight, the battery will supply the ECUs for up to half an hour meaning the pilot at least has chance to make a landing. Obviously, if the battery is knackered, that won't happen.
The battery being flat won't cause engine failure on its own - if the engines are running, the alternators will be working and supplying power. The problem occurs when the battery is weak and a large load is placed on the electrical system - such as raising the gear, which is what caused the crash in Speyer. The momentary power spike from raising the gear interrupted the supply from the alternators to the ECUs; the battery, being too weak, was unable to cover the drop in voltage, therefore the ECUs went dead and the engines stopped.