want to make iPhone notification device

I'm trying to make something like this that will notify me if I receive an SMS, email, etc. on my iPhone. If I get a bluetooth shield for my arduino uno, will I be able to connect my iPhone to arduino using Bluetooth 4.0 and send iOS notifications to the arduino and turn on an LED? Does the Apple Push Notification Service work with an arduino, or is an arduino even necessary for this project?

I don't have a lot of experience with electronics/programming- thanks for your help!