Redglobe,
My thoughts sort of go along with Bdgregory's view, except I maintain that it isn't the mat per se, but the entire turntable that matters with the mat, or mating surface, being the telltale area of concern because it is so near the beginning of the audio chain.
One oversimplified example would be that of tossing a coin onto a table. Would the resulting sound depend upon the surface of the table? Of course, it would. What if the table was unsteady? What if it had a loose board on top? Would that affect the sound of a coin striking it?
Now, put wheels on the table and roll it. Might you hear the coin rattling? Yes, you might. What if you taped the coin down? Would you hear it then? No, probably not. But, you might not hear it on a table that was designed and built better, even without the tape.
I submit that turntables are no different. A good one is solid enough to handle most resonances thrown at it. A bad one is not, except by luck. The record isn't perfectly interfaced, you say. Well, it takes two to tango, you know.
The platter and bearing assembly should be more than mere ways to look cool, and offer ad copy. Every minute aspect of them should be considered, including, among other things, the effects that a heavy ring clamp might add due to changes in inertia. If, however, the turntable isn't so great, go for it. Anything is an improvement, in that case.