Using SFINAE to check for global operator

I should have simply been more faithful to this answer.
A working implementation is:

namespace has_insertion_operator_impl {
  typedef char no;
  typedef char yes[2];

  struct any_t {
    template<typename T> any_t( T const& );
  };

  no operator<<( std::ostream const&, any_t const& );

  yes& test( std::ostream& );
  no test( no );

  template<typename T>
  struct has_insertion_operator {
    static std::ostream &s;
    static T const &t;
    static bool const value = sizeof( test(s << t) ) == sizeof( yes );
  };
}

template<typename T>
struct has_insertion_operator :
  has_insertion_operator_impl::has_insertion_operator<T> {
};

I believe that it does not actually rely on SFINAE.