Sure, any external HDD will work with Time Machine back up...as long as it's formatted in MAC OS Extended (Journaled) or NTSF. I prefer NTSF because it's MAC and Windows compatible, meaning you can use the stored files on both types of computers. If you only intend on using the back up files on a MAC then the OS Extended would be the better choice.
To read and write on an NTSF drive with a MAC you may need to install a driver, I use Paragon NTFS. It depends on your MAC, newer systems have the necessary drivers installed.