Nah, he's not going to die. That looks like a new injury with a touch a shell rot. That's very easy to treat and when he molts it'll be gone. It's only really an issue when you see it like this:
In that picture, the shell rot ate through the current shell, the new shell underneath and into the tissues. It most likely died because at that point, the shell often get stuck trapping the crayfish when if finally molts. And holes into the tissue allow for parasites and other things to get in and eat away at the crayfish.
But little injuries and little touches of shell rot, just give them salt bathes and keep the tank clean. It won't progress quickly when it's being treated and when the cray molts it'll be gone (remember to remove the molt though, you'll want to get the shell rot out of the tank instead of letting the crayfish ingest it from the old shell).
Edit: If it starts developing more or getting odd coloration, post more pics. Could be something else going on, but from those pictures at least, doesn't look anything to worry about too much.