You can, but the only ways you get dust is by disenchanting existing / purchased product or by earning it in arena. New players won't be good enough to earn it through back to back arenas, hell most good players can't do that, so they'll end up purchasing current product to d/e and craft old stuff. Considering to d/e a common you get 5 dust back but to craft one it's 40 dust i'd see that as a very expensive overall investment.
Now consider what has to be crafted to compete in Wild mode. Sludge Belcher, Dr Boom, Zombie Chow, Haunted Creeper, Shad of Naxx, Piloted Shredder, Healbot, Muster for Battle, Shield Maiden, Death's Bite, Lightbomb, Velen's Chosen. Just off the top of my head, of course it depends on the deck you want to build but it's still a lot of dust and even more if you want to go into more than one deck.