If you're concerned about someone gaining access to your backup. Then it is a good idea. Otherwise I wouldn't bother. I don't know if there is a performance difference. Probably not much since any semi-modern Mac should have hardware accelerated decryption/encryption with the CPU.
I only bother encrypting my laptop and locking the firmware. Because I want it to be a useless paperweight if someone steals it. Backups and desktops I'm not too concerned about since they are at home. Backups are stored in a safe when not currently backing up. Well secondary backups are in the safe. My primary backups are to my server. Also in computer to second internal drive on desktops.
Backup method is more important. Unless you really need the revision history with time machine. I'd suggest using Carbon Copy Cloner or SuperDuper. That way you'll have bootable backups. Backups are also way faster than Time Machine backups. Personally, I use FreeFileSync for manual backups. I don't need a bootable backup and it is really fast. The downside is that it is rather complex to setup.