Do any (or all?) torque converters disengage completely from the engine while the engine is idling and the vehicle is stopped, and/or the transmission is in Park/Neutral?
If a torque converter does not disengage during these stationary/idle scenarios, how much of a load does it add to the engine?
A torque converter is a fluid based device which transfers energy from the engine to the transmission. Unless otherwise modified, it is not engaged in the manner you suggest. An explanation is available here: How does a torque converter work?
For improved efficiency, many manufacturers are providing locking torque converters. These devices engage mechanically the engine and the transmission, reducing energy losses inherent in the un-modified torque converters, but they also require that below certain speeds and gear combinations to be disengaged.
You may discover complaint posts regarding motor vehicles which chug or buck or stall after exiting a highway. These are symptoms of a locking torque converter which has failed to unlock and behave in the manner of a manual transmission with the clutch engaged while coming to a stop.
The answer to your last question is that a locking torque converter which does not disengage applies maximum load to the engine, stopping it!
