Yes the -600 does have auto rudder trim, which is active as long as the Yaw Damper is engaged, it will hold in the event of an engine failure, even though I have only tried it in the simulator.
Without the yaw damper engaged it just a matter of correcting the yaw with the rudder pedals, and then engaging the yaw damper, which will then trim out any rudder force required.
The -600 is very easy to handle single engine, much easier that for example the -500.
However there is an risk of "lesser" pilots becoming reliant on this system for handling SE flight, and forgetting the basics.