I think the function of the sawdust is to allow the wood to dry slowly. It acts as moisture storage system. The whole mass slowly gives up its moisture until it reaches equilibrium with its environment. If wood, particularly something squirrly like burl or crotch wood, dries too fast the outside always dries faster than the inside. Drying causes shrinkage. Uneven shrinkage causes cracks. The problem is not one of drying, but of preventing cracks due to uneven drying.
Wood always dries faster on the end grain. This is where the wood is more open and moisture can escape faster. I always wax all the end grain (or any cut surfaces for burl). Some folks use paint but I lay the wax on pretty thick and get a better seal than paint will ever give.
AgMD