When you use Skype on your iPhone, and a non-Skype person calls you using your Skype-assigned phone number, does your phone ring like normal, though they're not calling your (in my case) Verizon-assigned phone number?
I may be wrong, and others can clarify, but you must have Skype running on the iPhone to get a call. When you get that call, the Skype program simply alerts you, in it's own proprietary way, to a call. This is totally unlike a regular phone call ring.