Obviously, they cannot be identical due to the encoding differences. In general a decent converting software will produce a result that sounds identical. If you are concerned make a duplicate of the file before you convert it. The software, however, won't overwrite the file unless you instruct it to do so.
I would expect the content of the binary will change due to encoding differences. Beyond that I would not expect any change unless you configured the conversion software to reduce the file size by degrading the audio slightly. But that isn't going to happen in a straight conversion except as a result of the chosen format, i.e, you might choose a lower quality sound format or a poor conversion program.