Empirically, we can look at something like CompCert, which formally verified a substantial section of a C compiler.
Subsequent high volume random testing with Csmith found no bugs in the formally verified section (unlike in every other C compiler tested with Csmith).
It should be noted that the verification performed was specifically about whether the compiler would produce incorrect code; cases where it would crash or error and not produce code would not be considered errors of verification. This would enable (for example) a coloring register allocator to be adjoined with some code that checked whether the coloring was correct and abort if not.
The problem with CompCert is that it produces really bad code, below the level of gcc -O0, about the level of the eternally-in-progress compiler project you worked on in your Programming Languages 370 course. So you can get most of the benefits of CompCert by running a standard compiler with -O0.