Does C++ compiler have to compile multi-threaded code with data race "as coded", or is permitted to do anything since undefined behavior is caused?

Let’s say I have hardware on which all the accesses to memory for a value less or equal to size of bool are thread-safe, and consistency issues in regards to caching are avoided because of the hardware or the code.

Should I expect that non-atomic access from multiple threads will be compiled just as the code was single-threaded and so I get the thread-safe program for the platform?

---

The question is FAQ-style, see my answer for it: https://stackoverflow.com/a/69062080/1790694