Compatibility of iPad Air with Peripherals
Apps can't be stored on an external drive1. In fact, not much outside of media can be stored externally, especially without jailbreaking.

With jailbreaking, you can mount the external drive as a volume with iFile, which lets you store files on there. However, many apps crash when attempting to access files stored outside a sandbox by means of symlinking due to security restrictions.

Basically, it's nowhere as simple as external drives with OS X. You won't be able to do much with an external drive, and even less if you don't jailbreak.

The iPad Camera Connection kit with its SD card reader and USB port was not designed for storing files from the iPad — it was designed to import media from a camera. There are specially-designed drives for iOS devices, but they're for storing media, not apps or app data.

1 Well, jailbreaking lets you move the app and move it back, but it can't be run from the external drive, and moving it will probably break the permissions (and springboard).