Function passed as template argument

Yes, it is valid.

As for making it work with functors as well, the usual solution is something like this instead:

template <typename F>
void doOperation(F f)
{
  int temp=0;
  f(temp);
  std::cout << "Result is " << temp << std::endl;
}

which can now be called as either:

doOperation(add2);
doOperation(add3());

See it live

The problem with this is that if it makes it tricky for the compiler to inline the call to add2, since all the compiler knows is that a function pointer type void (*)(int &) is being passed to doOperation. (But add3, being a functor, can be inlined easily. Here, the compiler knows that an object of type add3 is passed to the function, which means that the function to call is add3::operator(), and not just some unknown function pointer.)