The patch is not easy to read, but if it can be summarized to:

    if sysconfig.get_config_var('WITH_THREAD'):
        <build the _multiprocessing extension>
    else:
        missing.append('_multiprocessing')

then this makes sense - it seems that the multiprocessing module is
completely unusable if python cannot use threads. Even at the python
level, it uses "import threading" in many places.

This need another review, though. Raising issue to ReleaseBlocker.