Can the ‘crystal clear_cache’ command have a (very) significant impact on the size of the executable (and the compile time)?
Compile time, yes. When a cache exists, the compiler might be able to re-use previously compiled byte code. That might be noticable when building the same (or a very similar) program multiple times. But the effect is limited.
Executable size should definitely not be affected by the existence of a cache. If it is, something is going wrong.