Simple wire loop for detecting AC Mains activity?
Could I wrap a couple of turns of small-gauge wire around one of the
  wires delivering mains power to the motor, rectify and smooth it and
  detect the resulting voltage using an opto-isolator?


You are mistaken on how you think a magnetic field is produced by a wire and how to detect it with a coil. Basically, a wire produces a magnetic field like so: -



Now if you wrap wires around the current carrying conductor your wire loops "cut" no net magnetic field lines and no voltage will be induced. Field lines need to "cut" through the plane of each wound turn as per below: -



If you rotated the above coil through 90 degrees (moving the coil from the X=0 plane to the Z=0 plane), field lines no longer cut the coil and no voltage is induced. Ditto if you rotated the coil from the X=0 plane to the Y=0 plane.

So, with wires wrapped round the conductor you get no cutting-action. Unfortunately, the symbol for a current transformer does show it (incorrectly I might add) as wires wrapped around a central conductor but, in reality, the wires are wound in such a way as to run parallel with the current carrying conductor like so: -