If you have a noise that is say 24 dB down in the left channel and add the noise, 24 dB down, to the right channel, the combined volume will be 21 dB down or double the power, not double the volume.
Isolation is ALWAYS necessary when it comes to turntables. Turntables are vibration measuring devices and they do not care where the vibration is coming from. The environment is full of extraneous vibration from your refrigerator kicking in to the truck running down the street. People who live in NYC are very familiar with this problem. I call it environmental rumble, it is even a problem if you live in the country, only not as bad. People with turntables that are not suspended. Put your stylus down on a stationary record and turn the volume all the way up. You will see your woofer moving, shaking. The turntable is measuring the rumble in your environment. If I try the same experiment on an SME or Sota you will see nothing, no shaking at all. Any unsuspended turntable needs to be put on a suspension platform. With the weight of the turntable the resonance frequency of the suspension should be below 3 Hz.