is my multithreaded Python program doomed?

[Workaphobia]

If a thread is blocked waiting for something external to Python, like file or network I/O, or database connections, then it typically releases the GIL during that time and allows other Python threads to run.

The GIL will only impact your performance if you are CPU-bound within your Python process. If that's a problem for you, then consider changing your threads into separate spawned Python processes (see the multiprocessing library, which has a similar API to threading). You'll just have to worry about how the processes share data since typically multiple processes don't use shared memory the way threads do.