It's certainly possible to incrementally rewrite an OS distribution in Rust, or even smaller projects like glibc.
Anyone want to set up the infrastructure so it's easy to take a library or a .c file and start hacking, and see if you still get a working OS in the end? I suppose part of the problem is defining "working OS" -- I'm not sure I know of any great test suites that check to see that a GNU/Linux distribution continues to in GNUy/Linuxish ways, which is usually what you want for a large-scale rewrite project.