I have a function I want to be a coroutine, but it has zero yield statements, so it is just a normal function?
  
  You can distinguish it from a normal Python function by putting if False: yield somewhere inside its body. Another common trick is to put a yield statement after the final return statement. Bit ugly but oh well.

Yes. If a function contains the yield statement, calling that function returns a generator instead of executing its body. For example, here's defining and calling a regular function:

  >>> def foo_function():
  ...     print('In a function!')
  ...     return
  ...
  >>> foo_function()
  In a function!

  >>> def foo_generator():
  ...     print('In a generator!')
  ...     return
  ...     yield
  ...
  >>> foo_generator()
  <generator object foo_generator at 0x10321aa40>
  >>> next(foo_generator())
  In a generator!
  Traceback (most recent call last):
    File "<python-input-6>", line 1, in <module>
      next(foo_generator())
      ~~~~^^^^^^^^^^^^^^^^^
  StopIteration

  >>> for _ in foo_generator():
  ...     continue
  ...
  In bar!