If the activated ability resolves but the targeted artifact isn't destroyed (perhaps because it has indestructible or it regenerates), Hoard-Smelter Dragon will still get the bonus.

If the targeted artifact is an illegal target by the time the activated ability resolves, the ability doesn't resolve. Hoard-Smelter Dragon won't get the bonus.

If the mana cost of a permanent includes {X}, that X is considered to be 0.