It has not.

There has been work to verify a subset of Rust's logic - https://plv.mpi-sws.org/rustbelt/popl18/ - but the compiler itself is not verified, no.

It would be better overnight. But it would be even better if we had one NT like kernel and a new OS built from scratch with a browser (webkit) based ui.

If we could do this by waving a wand without downsides (e.g. all existing maintainers magically acquire Rust knowledge, etc.), yes it would be better. No question.

Seriously, people, you can find kernel bugs at will with kernel fuzzers like syzkaller from Google. Look at https://github.com/google/syzkaller/blob/master/docs/found_b... and weep.

If the Linux kernel writers all instantly knew Rust as well as they know C, then in 10 years they might produce something that is as functional as the Linux kernel currently is. In the process, they would lose everything that they could do over the next ten years to improve the Linux kernel.

You could claim that eventually the payoff would pay back the lost 10 years. But "eventually" can be a very long time...