The C++11 FDIS it says
If a virtual function is marked with the virt-specifier override and does not override a member function of a base class, the
Yes, the program is ill formed when override is added to any non-virtual function.
Generally, functions with differing signatures (overloaded), are as different as functions with different names. The example given in the Spec is not meant to imply that the function name effects override. It's meant to show the common error that override is designed to prevent.