Multiple independent Python interpreters in a C/C++ program?

[skip at pobox.com]

This question was posed to me today.  Given a C/C++ program we can clearly
embed a Python interpreter in it.  Is it possible to fire up multiple
interpreters in multiple threads?  For example:

    C++ main
        thread 1
            Py_Initialize()
        thread 2
            Py_Initialize()

Do I wind up with two completely independent interpreters, one per thread?
I'm thinking this doesn't work (there are bits which aren't thread-safe and
are only protected by the GIL), but wanted to double-check to be sure.

Thanks,

Skip