If the startup disk is copied in its entirety to an external drive, can that external drive then be used as a startup disk?
Yes you can you can use disk utilty to clone the contents of one drive to another but you can also use Carbon Copy Cloner.
You cannot use an external disk as startup disk if you drag and drop the system files as the permissions on the files might change leading to unbootable external disk.
So do not drag and drop the system files, only clone the disk into another disk as it preserves all the file attributes, permissions, owner, group, etc.
You can use Disk utilty 'Restore' feature to clone a drive. So suppose there are two drives A and B. I want to clone drive A to B so in Disk Utilty choose drive B then click restore option then choose "Restore from A" That's it! let it do it's job but if you want to clone a lively booted up disk then you will need a third party app like Carbon Copy Cloner.