Q: Can I restore my OSX directly to a new, virgin external hard drive from my Time Machine or online Recovery...?

There is no online recovery for Snow Leopard, disc only.  You can install to an external drive connected to your computer while booted to the disc.

Time Machine backups do not have a copy of the system files and are not bootable. You will need to install using the system optical disc.

Try using a cloning program to transfer the data to the external.

Clone  - Carbon Copy Cloner          (Often recommended as it has more features than some others)

Clone – Data Backup

Clone – Deja Vu

Clone  - SuperDuper

Clone - Synk

Clone Software – 6 Applications Tested