Can python do this?

[Ken]

Is it possible to have a program running (either C or Python) and have
that program dynamically load Python functions while its executing?

The idea is to have a server running that users can connect to, and be
able to change functionality without having to restart the executable.
Objects/variables loaded into memory (ie. who's connected) would
also need to be saved.

If it is possible, would it be terribly difficult?