Power conditioners and wall warts

If your particular conditioner has fully isolated banks of outlets, then surely this isn’t a problem (plugging one straight in, I mean).

I have any some success reducing noise when plugging a switching power supply into a power conditioner. Audible results most often with turntables. Power conditioners can also ensure the power going into the switching power supply remains clean and stable.

for serious music listening I unplug all wall warts in the house and unplug my video system (from Charles Hansen of Ayre) 

Makes sense. But my turntable is powered by a wall wart. 

Chuck, you can use a linear power supply (LPS) and get rid of the wall-wart. A LPS uses a toroidal or R-Core transformer instead of the switched mode PS found in the cheap and noisy W-W. The result will be a significant improvement in sonics; better dynamics and detail, larger soundstage, lower noise floor.

You just need to know the voltage and amperes needed to run your TT.