My worry was that it is easy to make a write() method that does not return anything, but is still useful in most cases. Since BufferedIOBase.write() has to guarantee to write everything, it may not seem important to return a value. But we could explicitly check for None as you suggested.
In the BaseHandler class, each chunk yielded by the application is passed to BaseHandler.write(). But that method calls self._flush(), which should avoid any buffering problem. SimpleHandler._flush() implements this by calling self.stdout.flush().