It would be nice to see an effort to migrate some of the kernel core, but I can't see Rust gaining widespread acceptance in the kernel development community any time soon.
I don't even think that a migration effort from C -> Rust for the Linux Kernel is even feasible or even worth it, given the scale of the project. At this point, you might as well start from scratch.
Google is already experimenting with Rust for OS development with their new Fuchsia operating system [0], which has some drivers written in Rust with a capability based security model.
Similarly, Firefox's Project Quantum seeks to bring Rust to Firefox from the more experimental Servo project.
There are 2 reasons the Linux kernel in particular uses C and will continue to use C: 1) it was C originally and 2) it should compile without requiring some other compiler.
Anyone who sets out to write a new OS kernel (or similar) today for platforms where Rust is available, would probably/hopefully use Rust over C. That doesn't mean it's a good idea to start making existing code bases "hybrids". No one wants a huge codebase where to build it you need N compilers for languages that were popular in various times during the code bases hisory, and where you need to be an expert in N languages to maintain it.