Why would it? Using twisted (or py3's asyncio), the event loop is spinning, there is no thread for Python to be switching to. Except that we're using a thread-pool of course (to make external blocking network calls), and those threads are.... making network requests, which is I/O, and the GIL releases during that.
On a network bound daemon, which is not CPU-bound, the GIL is really not an issue, so it never came up.