Common sense tells you that it will dull down the vibration. Don't go on what some guy once said, use your brain.
Which guitar manufacturer puts a sheet of plastic under their bridges? Non of them do, the bridge is always mounted directly to the body.
Gibson and Fender have been making and toying with the operation of those guitars for 50 years, when you see one of those guitars in a shop, some might have bad finishes or whatever, but they are designed to produce the maximum tone and sustain from that model.
The ideal is a good sturdy bridge, mounted straight to a flat body, with a tight neck fitting.
Anything getting in the way of this will hamper the sound.
When you hit a string, the vibration runs across it's length (from nut to the saddle), but obviously, it transfers to the bridge too, if you have a piece of plastic under the bridge, it's trying to vibrate that too, but the plastic will kill the vibration equalling reduced sustain.
Are you saying that this wouldn't occur?