C++ can compilers inline a function pointer?

Suppose I've got a function functionProxy that takes a generic parameter function and call its operator():

template< typename Function > void functionProxy( Function function ) {
    function();
}

The object passed to it may be:

• a functor:

  struct Functor {
      void operator()() const {
          std::cout << "functor!" << std::endl;
      }
  };
  

• a function:

  void function( ) {
      std::cout << "function!" << std::endl;
  }
  

• a (C++0x) lambda function:

  [](){ std::cout << "lambda!" << std::endl; }
  

int main( )
{
    functionProxy( Functor() );
    functionProxy( function );
    functionProxy( [](){ std::cout << "lambda!" << std::endl; } );
    return 0;
}

Will the compiler be able to inline function within functionProxy in all the above cases?