Is there a non-electronic turbo diesel engine?

Yes, more than there is electronic turbo diesels.

If the alternator and battery is disconnected after the diesel engine has warmed up, will it still continue to run?

Electronically controlled diesel have ECU, sensors and actuators that depend on electricity, these componenets is vital to the operation of the engine.

But I heard of instances/emergencies that an electronic controlled diesel engine cannot be shut off even if these batteries where disconnected.