Among other things, one reason for liberal use of const that I've seen is that, by ensuring that the value won't change, the compiler can more effectively optimize the resulting code. This seems reasonable (but I've also heard that the benefits of this are somewhat minimal).
In any case, would be same be true when working with stateless classes / objects? Could you reasonably expect even a minor speedup from marking stateless objects const, or are today's compilers good enough to recognize statelessness, and optimize for it regardless of whether its marked const or not?
Feel free to answer either in terms of specific compilers, or compilers in general.