Will Time Machine backup of an encrypted HDD be encrypted?

Solution 1:

No - Time Machine will not preserve the encryption of the source disk since it reads the files in an unencrypted manner just like any other process once you log in to the Mac.

You would need to ensure that all Time Machine destinations are also encrypted to properly secure your data both on the main computer as well as have it encrypted on the Time Machine volumes. This is as easy as ticking a checkbox on the Time Machine preference pane in system preferences.

On macOS 10.12 Time Machine will throw a helpful notification if you do in fact select an unencrypted destination for encrypted OS.

Solution 2:

Mavericks does encrypt backups. From Apple:

The best way to keep your backups secure is to encrypt your backup disk. Encryption is available for Time Capsule, disks attached to another Mac on your network, and disks partitioned with the GPT partition scheme and attached directly to your Mac.

If you want to change from unencrypted to encypted backups, you must remove your backup disk and then set it up again.

So, if you have an existing backup, you'll need to remove them from the backup disk you'd like to be encrypted. You should be able to see the encryption status of your backup on a per-volume basis in the Time Machine pref pane.