Would you please share your technique as to how you encrypt a TM-linked directly-attached drive? Assuming your internal HDD isn't encrypted for performance's sake.
You can encrypt a drive using Core Encryption by just right-clicking it on the desktop and choosing "Encrypt...", which will then lead you through the process. It takes a while, but happens in the background. I don't think there's any real performance hit, by the way, in encryping your internal HDD (or SSD), because from what I understand the encryption takes place at a very low level in OS X.
Also, if you did encrypt your boot drive and cloned to an external, that clone would NOT be encrypted — it's just cloning the actual data. You'd want to encrypt that external drive separately as described above. I do this because then I can keep the clone at work or anywhere really and not worry that anyone will be able to open it up and rummage through all my junk.
I would note that I'm not encrypting my Time Machine drive, I'm encrypting the drive I clone to every month (not with Time Machine, but with Carbon Copy Cloner).