And that makes three opinions that the finish on a plinth matters not, save for aesthetics.
In musical instruments the wood is part of the equation as both Nate and Al have said. It's meant to resonate.
Exactly the opposite of what you're looking for in a plinth. You're looking for the mass of wood to absorb resonance, just as Nate has stated.
Personally I'd recommend a sealer coat, and 3 or 4 top coats of an oil based finish. These are my favorites, as they have modifiers that improve durability as well, but still have the depth and sheen of a great Tung oil finish.
Buy Seal-a-Cell Clear Finish, Quart, GENERAL Seal-a-Cell Clear Finish, Oils -
Buy Semi-Gloss Arm-R-Seal, Quart, GENERAL FINISHES Arm-R-Seal, Oils -
I've used these products on my own plinth with outstanding results.