Can I make an entire game in Unity 3D for the iphone without using any Objective - C or Cocoa?
Yes, but you're limiting your options. If you want to include things like OpenFeint or analytics you're going to have to go through the native code plugin bridge.
There are also some new things in iOS4 that aren't handled properly by Unity iPhone by default, like the resolution of the iPhone 4, or the application callbacks by task switching.
The short answer, is Yes, you can definitely make an entire game in Unity3d. Many developers have.
RE the previous answer: actually, for analytics, this link will take you to a C# integrated google analytics helper for Unity 3D http://www.persistentrealities.com/code/
And now with Apple's "Game Center", you might be able to skip Open Feint integration, though I still prefer Open Feint for now, personally.