Yes, different types of baking stone will be more efficient in pulling moisture from the dough as it cooks.
While I do agree that different materials DO absorb different amounts of water, the most common commercial stone material, cordierite, is so dense that the amount of water that it absorbs is marginal. Furthermore, the temperatures of the pre-heated stone are sufficiently high enough that any water contacting the stone isn't going to be water for long.
I've seen tests comparing cordierite and soapstone (no absorption) and the results were marginal. You could barely tell the difference. I've actually started recommending completely non absorptive steel plate as a super conductive method of overcoming the anemic conditions in home ovens that can't go above 525 f.
There are cast refractory stones available on the retail level (fibrament), that, because they are cast, they're very porous, but this porosity trashes conductivity (the kiss of death for the home pizza baker seeking shorter baking times) as well as shortens their longevity. As water converts to steam it expands 1600 times. For the sake of durability (and conductivity), one doesn't want
a more absorptive stone.
So, imo, more/less absorptive stones are not the answer to crispiness issues.