I guess it is a background mode related to ExternalAccessory.framework.
But the document about External Accessory says, "If your app is suspended in the background when an accessory notification arrives, that notification is put in a queue. When your app begins running again (either in the foreground or background), notifications in the queue are delivered to your app. Notifications are also coalesced and filtered wherever possible to eliminate any irrelevant events. For example, if an accessory was connected and subsequently disconnected while your app was suspended, your app would ultimately not receive any indication that such events took place.".
This means that the external accessory communication will be just queued until the app enters foreground mode, But the other background modes like Location, Bluetooth LE are working as real-time in background mode. So I doubt that just queued is the only thing that can do. Is it really?
If your external device is "Made for iPhone/iPod/iPad" - MFi you can use this option. It's not for BLE communication.