Will corruption auditor work if ETag is ommitted?

From the notes:
"You can ensure end-to-end data integrity by including an MD5 checksum of your object's data in the ETag header. You are not required to include the ETag header, but it is recommended to ensure that the storage system successfully stored your object's content.

The HTTP response will include the MD5 checksum of the data written to the storage system. If you do not send the ETag in the request, you should compare the value returned with your content's MD5 locally to perform the end-to-end data validation on the client side."

So what happens if the client does not send the ETag? Will the system still be able to find bit-rot, or other forms of corruption? It says it is recommended to check that it was stored properly, so that to me is just a time-of-write check, but what about data-at-rest periodic checks?

And if there is no ETag, how does the system know which version of an object is valid if it is in 3 different zones and they are all different versions of the file (let's say because of corruption).

Thanks!