Importance of power cable for Turntable?

The motor is a source of EMI which can affect  components sharing the same AC line or by direct radiation from the motor or its power cord. So if a cord provides good shielding and/or has built in filtering, its possible you’d benefit.
 

Thanks All.  I had heard the first argument already (from Elizabeth) but was also wondering about “pollution” of the AC line caused by the motor, with the AC line being the same line my amp is plugged into.  Unfortunately my amp and eventual turntable when I get it will be plugged into the same AC circuit in my house.

I wonder, would something like a Furman 8D be better than a power cord upgrade for the turntable......  essentially blocking the noise from the motor from entering the AC circuit.  And would cost way less than the PC upgrade....

While all this thinking about noise from/to the table may be true (or may be better addressed by other steps as the OP suggests) my experience is that even when the AC is treated (as in my system) by multiple levels of filtering well before the power cord to the table it still is the case that changing the power cord to the table adds benefits. The effect is similar to a good power cord on an amp -- more stability and attack, more ease as the table is subject to wide dynamic swings, a crisper presentation etc.

All of this is icing on the cake in an optimized system but if that's where you are heading, and you have a power cord handy, do try one -- the effects are likely to be additive to whatever else you are doing (and that's before getting into the benefits of footers and other vibration control effects on the TT PSU as well ...)

Of course I may well be totally lost in tweakery woo land ... but that's the territory we're operating in now

Wow!  Okay I’m hoping not going to quite that crazy with power mgmt lol!

Have to point out the slight irony in all of your power mgmt lengths you have taken but use a stock cord to the turntable!  Probably makes sense though.