I am creating an iPhone app utility that would benefit from some 3D in places.
Instead of learning OpenGL, is it possible to export 3D models, textures and animation from Unity3D and control the animation in the Objective-C code?
No, you either use Unity for 3D or you don't; "exporting OpenGL" is not something that exists. If you're asking about having a "standard" app that has some 3D elements instead of doing the whole app in Unity, then yes, you can write Objective-C/whatever in XCode, and have that interface with Unity. But all the 3D is done in Unity.