I did add a high gage dedicated line and didn't hear a difference. As you have a relatively quiet load unless you have a significant distance of travel I doubt you will hear much either. Voltage drop is your enemy related to distance. There are tables to show you this and mine was 100 ft which drops a bit.
Did it myself for a couple of hundred. Inspector cared more about a child proof receptacles and the distance between wire attachment points. Was sort of snarky with me putting in the heavier wire but justified himself by saying, well I guess that is all you had. He was more impressed with the LED recessed lighting I added to around the room near the room edge.
I then added a regenerator, not a power conditioner and it was night and day. My advice would be skip the dedicated circuit if it is going to cost more than a few hundred, and invest in a regenerator which just plugs in the wall. It will normalize your voltage, no drop, patches up the tops of your sine waves, and fills in for any quick current transients. Will be such an improvement that even my wife hears the difference