The new Bluetooth 4.0 Low Energy (hereafter BLE 4.0) specification which is implemented in Apple's latest iOS devices does allow one to create app-specific profiles and connect to BLE 4.0 devices without jailbreaking, using an approved Bluetooth 2.1 profile, or becoming part of Apple'd MFI program and using the previously required MFI cryptographic chips.
In other words with the proper BLE 4.0 compatible bluetooth radios you can create wireless devices that connect to iOS apps without having the device pre-approved by Apple. However, you must write a custom app for the device, and Apple still holds the ability to reject that app if they want to. So they still control this to a great degree. This is essentially Apple's answer to the Android ADK, while not fully relinquishing the ability to shut down apps and devices they don't like.
Your app must include specific XML schema for your app's bluetooth profile, and use CoreBluetoothFramework APIs, so it's very obvious to Apple during the app approval process that your app connects to a device. If your app does not work without the device present, then it's likely to be rejected if you are not part of the MFI program, as Apple cannot test the app without your device. The apps that appear to be successful in passing this test use the device as an accessory to app functionality, rather than a requirement. For instance an exercise app might connect to a BLE 4.0 heart rate monitor, but the app doesn't depend on it.
Some apps seem to be getting around this by displaying simulated, or online information in place of the device information when no device is present. Thus the app can be tested without the device, and functionally works when the device is present.
You can find out some successful efforts online:
http://blog.makezine.com/2012/03/19/bluetooth-4-0-from-arduino-to-iphone-no-jailbreaking-no-mfi/
BlueGiga in particular has been pushing their devices specifically for this use, so there are probably forums and support for this elsewhere.
Keep in mind that the devices that currently support BLE 4.0 are limited, and currently only include
- iPhone 4S and later iPhones
- recent MacBook Air, Mac Mini
- iPad (3rd generation and later, and iPad mini)
- Macbook Pro Retina
There may be other Apple devices that support this standard, it's something Apple is advertising openly on each product's technical specifications page so it's easy to find for current products.