Do they continue to charge you even if the server is powered off?
Discussion
Yes they do. They give you a big warning say that you will still be charged even when your droplet is off. You have to destroy the droplet.
What you could do but I haven't tried is after you destroyed the droplet is create and exact droplet in terms of hardware and restore a snapshot or backup to the new droplet.
Snapshots and backups are cheap to store.