How feasible would it be to compile Python (possibly via an intermediate C representation) into machine code?
Presumably it would need to link to a Python runtime library, and any parts of the Python standard library which were Python themselves would need to be compiled (and linked in) too.
Also, you would need to bundle the Python interpreter if you wanted to do dynamic evaluation of expressions, but perhaps a subset of Python that didn't allow this would still be useful.
Would it provide any speed and/or memory usage advantages? Presumably the startup time of the Python interpreter would be eliminated (although shared libraries would still need loading at startup).
Try ShedSkin Python-to-C++ compiler, but it is far from perfect. Also there is Psyco - Python JIT if only speedup is needed. But IMHO this is not worth the effort. For speed-critical parts of code best solution would be to write them as C/C++ extensions.
As @Greg Hewgill says it, there are good reasons why this is not always possible. However, certain kinds of code (like very algorithmic code) can be turned into "real" machine code.
There are several options:
After that, you can use one of the existing packages (freeze, Py2exe, PyInstaller) to put everything into one binary.
All in all: there is no general answer for your question. If you have Python code that is performance-critical, try to use as much builtin functionality as possible (or ask a "How do I make my Python code faster" question). If that doesn't help, try to identify the code and port it to C (or Cython) and use the extension.