Is this possible? If so, how?
Do you mean, when previewing your own reply, you see a new reply pop up in the thread that happened while you’d been composing your post? If so – yes, it happens a fair bit.
You can’t really preview someone else’s reply.
I think he’s asking “can someone read what I’m typing/editing/previewing before I post it”, and the answer is “no”. Nothing is written to the database until you actually submit the post.
Well, if you happened to be standing behind the person typing and looking over his or her shoulder…
Did anyone else, reading MEBuckner’s post, just look over his shoulder?
I knew you were going to post that, TTT. It showed up in MEBuckner’s preview a full 30 minutes before you even typed it. 
There might conceivably be some way that the administrators could monitor stuff being previewed - the post to be previewed is sent to the board server (rather than formatted locally), so they probably could set up a process to intercept it and copy out to a text file or something, but it might involve hacking the board software and I can’t honestly believe they would have much inclination to wade through mountains of half-formed posts.