When you compile a Unity project for iOS it takes your C# or JavaScript code and AOT compiles it to a native dll. It then creates an xcode project which loads that dll. You can add native objectiveC, or C/C++ functions to this project and expose them for calling from the Unity engine.

http://unity3d.com/support/documentation/Manual/Plugins.html

Unity also has built-in methods for accessing URLs.

I don't know how the Unity SDK is built, but if it's a static Objective-C library then you can access iOS SDK functions without any problems. If its a script engine where you develop your scripts outside the IDE then you may not access iOS function.

Have you checked other engines/sdk's for your game development? I know that Cocos2D is well documented and I know for sure that you can call iOS methods. Good luck!

I used both unity3d and corona which are very good at their field, and yes you can use all standart SDK over them, sometimes you need to do tricks though (which is quite a pain). If you are developing a 3d game and familiar with NVIDIA PhysX engine go for unity, it gives you nice features. But if you are clueless about collasions/rigidbodies/ragdolls etc you would have a hard time for sure.

As for 2d application development since I don't like Objective-C I prefer corona which you code in lua (easy to learn and use). You can use most of the IOS SDK in it without any problem.