The use of a multiengine aircraft’s throttles for steering and pitch control is critically important should the aircraft’s primary flight controls fail or severely malfunction; are pilots nowadays taught this potentially-lifesaving skill during training for a multiengine rating?
No. In a piston multi course the focus is on flying the airplane and single engine procedures. Loss of rudder control in something like a Seminole is not a big deal unless the engine quits after that and then you have a problem, and it's not one of controlling yaw with differential thrust.
If your rudder cables broke with both engines running you would naturally use bits of differential power to center the ball as required while flying straight, and little rudder is required to turn so that's not a big deal and you would just leave it and put up with a bit of adverse yaw. This all wouldn't require much training to figure out.
Sioux City was what you would call a freak event, with multiple simultaneous failures of flight controls for all axes, that is not catered to in design in the first place (notwithstanding the mistake, on the DC-10, of running all the hydraulic lines though one choke point; most airplanes separate control runs as much as possible to cater to turbine burst events). They were trying to control both pitch and roll, with differential thrust to turn by skidding and by using the pitching moment of increasing/decreasing thrust to climb/descend.
No type course trains for that. There are a million one-of-a-kind events you can dream up, which can theoretically happen, for which airliners are not certified to cope with, and where a crew might have to figure things out on the go. If you had to train for all of them, the type course would take years to complete.