Yes, the iPad (or iPhone) can act as the only display for a Mac.
To setup Duet to display as the only screen, first install Duet's Mac application with another display and then disable your account login screen. This step is necessary because Duet is not able to load until after the login screen. With this setting the Duet Mac app will load when waking the computer from sleep, during startup or after a restart. To do this go to System Preferences > Security & Privacy > uncheck the box "Disable automatic login". Then go to Users & Groups and click Login Options and select Automatic Login: On
If you have any issues with Duet connecting at startup or after waking from sleep please check that "Launch at Login" is enabled in Duet's menu bar app preferences and that Duet is a login item in System Preferences > Users & Groups > Login Items. If Duet is not present as a Login Item, enable it in Duet's Mac app preferences and log out or restart your Mac to add it back.
OS X will prevent automatic login if you have FileVault encryption enabled (found in System Preferences > Security & Privacy > FileVault) or iCloud Keychain enabled (found in System Preferences > iCloud > uncheck Keychain.
If you are still not able to login you may need to purchase a monitor dongle. Some older Mac and Mac Mini models require a physical connection to be registered in order to startup and login. For more info please check this link: http://blog.macminicolo.net/post/72706369716/an-hdmi-adapter-for-a-headless-mac-mini
Alternative Login Option for Additional Security
If you are security conscious and want to use a password, you can use OS X's Name and Password login to login with only keyboard input. Warning you will not be able to see the display until after you've logged in successfully.
System Preferences > Users & Groups > Login Options > (click the Lock to make changes) change to Name and Password login.
1. Type your username and then hit tab
2. Type your password and then press enter to login