I have spoken to Ed about this in great length, as we collaborate on the PPT mouthpieces which were originally made in Ed's normal resin, then we offered a Bronzite alternative. I now only make them in Onyxite.
Ed believes that the material makes a difference in any part of the mouthpiece tha vibrates. Most of the mouthpiece does not vibrate, but if the tip is this enough, then it would vibrate and act almost like a double reed.
What this means in real terms of mouthpieces out there is that if the tip is thin enough it will possibly vibrate, so having an effect on the sound. Most HR mouthpieces have a lot of material at the tip, too much to vibrate. A metal mouthpiece can have more or less material there. It can have less because metal is stringer, possibly it can be thin enough to vibrate in a way that an HR couldn't because if you made it that thin, it would not be strong enough.
My belief goes along with this. If you can make a mouthpiece with really thin material at the tip that won't break, then yes, that material might affect the sound. However it's unlikely anyone could ever conduct a conclusive experiment to prove or disprove this theory. Until then I make mouthpieces using a material that looks good, is easy to shape into the best sounding shape, and does not poison you.