In order to use XNA you'll have to have the hard drive, end of story.
From the FAQ:
Q: Do I need a hard drive to run XNA-based games on my Xbox 360 console?
A: Yes. The XNA Framework runtime environment for Xbox 360 requires that a physical hard drive be present on your Xbox 360 retail console.
Andy,
It is still too early to offer firm details about XNA Game Studio Professional (other than what is answered in the FAQ).