Does a turntable mat make any difference?

The Funk Firm Achromat is one of the greatest mats available. I have used it on high end Rega P10 and Linn LP12. It DOES a make a significant difference . Bass is tighter and the high notes clearer. The Linn dealer was skeptical and when he heard it he fully agreed that it made a great difference compared to the Linn felt matt. Same for the Rega. On top of it, it reduces static build up. Great product at an affordable price! 

If you're talking about a difference in sound, absolutely not.

If your VPI tonearm is wobbling....install the 2nd. pivot

The purpose of the platter/mat is to provide a stable surface to mate with the vinyl.  The energy induced into the vinyl by the vibrating stylus should be effectively transmitted into the platter/mat.  Therefore, soft or pliable mats are a poor choice.

I have found mats of aluminum and copper in combination with center and periphery record clamps to effectively absorb induced energy.

Absolutely makes a difference to me on my TW Acustic TT, but who knows what it will do for you in your system. My favorite is a SPEC AP-UD1 Turntable Mat. No static, not overdamped, not too thick, and not too heavy.