If it is defined as an error, but the compiled build will continue to run with the value wrapped around, I would say that's indistinguishable from UB.
No. An integer getting deterministically set to an unintended value is a bug. A bug is not the same thing as UB. (Even if it were non-deterministic, it would still not be anything like UB.) It's not the same ballpark, not even the same sport.
It's indistinguishable from unspecified behavior, not from undefined behavior. Unspecified behavior has to pick from a finite list of allowed behaviors. Undefined behavior can do anything.