Can a user who is not a Moderator see the deleted chat messages from other users?
Yes: In addition to moderators and the originally posting user, the room owners (of the particular room) also have access to the history of deleted messages.
However, unless the message's
(removed) stub is right there visible in the chat room (in which case you can click "history"), you'll have to manipulate URLs by hand. This is intentionally designed to be not too simple a process.
Nobody else can see them, though. In particular, this is not related to reputation (unlike the ability to see deleted rooms).