The headline of this article is misleading. Markets don't 'fuel' demand. They match existing demand with supply. The demand comes first, and exists in the mind of those who want to buy ivory (or drugs, or whatever the case may be).
My favorite example is "collectable computers" since I lived this during the late 90's and early naughts. A lot of people wished they had that old computer they learned on, or wanted desperately as a kid, but circumstances had kept them from it, and they had largely resigned themselves to never owning one. And then Ebay happened. And it created a market that allowed sellers from everywhere to put what ever crap they wanted to "online" to a wide variety of possible buyers. And suddenly, people had a way to actually service their desire for an old computer.
Altairs, IMSAI's, PDP 8's and PDP 11's. Stuff that was "worthless crap" could find someone who would cherish it and pay for it. I found myself buying pallets of stuff from SRI's "junk" sale for $50, only to sell the 10 HP calculators in a box on that pallet for $2,500 on EBay, old PDP parts to collectors for $300 - $500, and just playing with a really nice set up custom built instruments.
So did Ebay "fuel" the demand? It certainly felt like it from a non-economist point of view. It was the only thing different now than before. But no, the demand was out there and Ebay simply made the market for it.
The Ivory market is the same way, its constrained to legal sources but the demand exceeds those sources. If there was no market for ivory the demand would remain boxed up, with people who wished they could having something of ivory but won't cross the line of legality to get it. That demand would go dormant. And many times it has been proposed to do just that, ban all ivory sale and transport. And that would hurt the poachers, but it also would hurt the folks who have "legal" ivory and could benefit from converting it into cash. The solution to both problems simultaneously still eludes us.
If there was no way to acquire legal Ivory and all forms of Ivory would be illegal and culturally unacceptable people would want it less, if it will be viewed as morally abhorrent to have an Ivory statue as a center piece in your living room less people will want it.
If artists could not get their hands on Ivory they will result in using alternative materials, most people don't want a block of Ivory they want a masterfully crafted art piece again driving the overall demand for Ivory down.
Markets are not static entities that exist on top of some underlying substrate of supply and demand. Supply and demand change according to market structures.