I remember this stuff being discussed some years ago.
It seems that exotic materials like this are sometimes brought into the theoretical mix with the assumption that if it excels at it's specific design function(s) it will be wonderful for speaker enclosures. To my way of thinking speaker box material only really needs to accomplish a couple of things; a place to mount drivers and contribute nothing of it's own to driver output... IOW, a dead box. A gilded box will sound the same as a raw one...no?
MDF seems to be nearly tailor made for the job. It's inexpensive, easy to work with and has good internal damping qualities. I suspect that when some commercial speaker builders tout some exotic material as their secret sauce, its as much marketing as it is anything else.
Corian is a brand name within a group of materials known as solid surface. Solid surface essentially comes it two flavors; polyester resin and acrylic resin, most commonly available in 1/2" thickness. Different manufacturers have proprietary recipes, but that's more about appearance. I've never build speakers with it but if you take a piece of it, suspend with a pair of pliers or similar and tap it with a hammer, it definitely has a ringing quality that would not seem very well damped. If I were to speculate, I'd guess it would resonate at higher frequency than MDF which would seem to be harder to deal with, design wise. My intuitive guess would be that you'd have to have substantially more thickness to get same damping qualities as 3/4" MDF.
I'll qualify the above by claiming off-the-cuff science...I'm a seat-of-pants engineer.
