Can I develop a service on iOS to register with ANCS so that when iPhone gets a notification the service go through my device BT LE protocol to notify the band? And I read a
Correct. As the link mentions, you use "service solicitation" to get the iOS device's attention while it is passively scanning. You don't need to have an app running on the iOS device, you don't need to submit anything to the App Store--you don't even need to pay to become a developer. Also, I should mention, your hardware design does not need to be submitted to the Apple MFi program.