What I thinks I am really asking is a long cord voltage drop similar to
after-market devices that slow down motors like a router?




Similar, you're limiting the current though rather than effectively
using PWM so you'll get less torque with voltage drop than with a speed
controller, the motor shouldn't heat up more than usual though.

Induction motors on the other hand will overheat if the voltage drops.
They're constant power devices and lower voltage will cause higher
current to be drawn to compensate, higher current = more heat.