Can I back-up my Mac and an attached external drive with Time Machine?

John Galt is correct, "all connected [MacOS formatted] drives" is the default. [Windows drives require their own backups.]

To check, just click the (Options) button, and take a look at the "excluded" list. if your external drive is Not Excluded, it will be backed up.

By default TM backs up all mounted volumes, with the exception of the backup drive itself (which cannot be backed up).