I'm not sure how much impact this would have if you were using a TT with a DC Servo controlled motor, but if you have an AC Synchronous motor clean power is an absolute must since the motor uses the AC wave as the timing source for speed control and any noise on the power will directly convert into sped instability. AS for plugging a speed controller into a power conditioner I would have to say it would really depend on the controller and the sophistication of the power supply within. My VPI PLC drops the AC down to DC and then regenerates an AC wave at the frequency you specify. In theory this should isolate the output from any input noise, but I have seen the schematics for the unit and the circuitry is not very sophisticated so I can see some noise leaking through. I is still way better that plugging the motor straight into the noisy AC, but I can see the possibility of further improvement with a cleaner AC input. And what the heck, if you already have a conditioner, it won't cost you anything but a little time to find out.
I'm not sure if the same thing would hold with some of the newer more sophisticated speed controllers. For example the VPI PLC was replaced by the SDS which is three times the price and contains much more complex circuitry. However, more complex regeneration circuits do not necessarily mean it also has a better power supply, it might, but I have not first hand experience with the unit, so I can't say for sure. Anyway, the same thing hold for this as well. Anyone who is concerned enough with SQ to buy one should be willing to take the time to do a little experimentation to see if any kind of power conditioning before the speed controller would help. Maybe yes, maybe no, but it would sure seem to ne worth spending a little time to find out.