If you save with these options set
You will get a binary copy, same size and checksums, but the Modify date of the new file will be Now.
Some programs (IrfanView, ExifCleaner spring to mind, maybe Audacity too) provide an option to preserve the Modify date even though they modify the file - in place or a separate a save location.
And of course a file copy/move via the cmd line or a file manager will preserve the Modify [content] date but set Create [file] date to NOW - which confuses more than a few people.
BR