the answer is no, you cant rewind a match you just started watching. The moves are stored on your interface, so you only have what you were there to see.
The bot you describe is certainly possible, but a lot of work, for potentially little use.
You are more than welcome to code it, and then talk to Patti about running it. The rules seem to be that it can be there, as long as it identifies itself as a bot, and serves a useful purpose or need in the community.