Sure, but I think that is the point. You can do that, but its not as convenient and becomes harder to read. And besides, those are free functions you speak of, not closures. To emulate multi-line closures becomes even more obtuse.
Sorry, I edited my comment and you may have missed it. How would you emulate multi-line closures in Python? A free function which you can pass to a higher order function is not a closure. I think you would need to create a functor, and that becomes even more verbose.
Closures are functions that can capture values/references visible in the scope where the function is defined/instantiated. They are basically a short hand way of creating function objects, functions which have data members.
I believe all functions are object in python, so you can add attributes to them, but you'd be better of creating a class with a __call__ method. Relevant scope can be captured in the class __init__.
Classes themselves can hold multiple functions/methods, and if you want a function that carries state, maybe a generator would be useful?