Speaking as a compiler developer: compilers for standard languages make no attempts to guarantee constant-time properties, nor to provide any primitives that can be used implement constant-time guarantees. Indeed, the developers are likely to be moderately hostile to proposals to add such primitives--it is a pretty different beast if you're worrying about constant-time.

As such, if you're using a standard compiler for a language to implement a constant-time guarantee, you need to be doing verification of the resulting assembly to make sure that it actually is constant-time. If you're not doing that, or you're not verifying the generated assembly itself, your constant-time guarantee is not worth the paper it's printed on. Even if it's not even printed on any paper.