If the target permanent is an illegal target when Topple the Statue tries to resolve, it doesn't resolve. You won't draw a card. If the target is legal but isn't tapped, isn't destroyed, or is neither tapped nor destroyed, you do draw a card.

Topple the Statue can target any permanent, even one that's already tapped.

If Topple the Statue targets an artifact, that artifact will be tapped if it's untapped, and then it'll be destroyed. Any abilities that trigger as it becomes tapped do so and will resolve after Topple the Statue has finished resolving.