Rat's Register Allocator

Do compilers use profile information to allocate compilation time (such as by using an extremely expensive but slightly better register allocator for a hot loop)?

I got the impression that expensive register allocation is not an option. A 1% improvement in register allocation that results in a 0.1% local performance improvement and a 0.002% program performance improvement may be considered not to justify 1000x local compile time, but for frequently run stable-ish software the compile time and compiler development/maintenence time might be justified.

(I am not a programmer, but I do like thinking and learning about such things.)