Yes. You can watch something loosely similar in the form of people's let's plays on youtube, but it might be kinda cool if someone put together the footage in a more planned way.
Off the top of my head, this would involve carefully controlling Marty to walk only in ways that make perfect sense for the moment (including taking a pause to think when he'd need to in-character, or turning and walking in a specific direction at a given time, that kind of stuff). Also making sure that the cursor was not displayed on-screen (you'd need to use a recording program that hides it automatically).
Besides that, it would mostly involve making sure you don't skip any important parts, and that you get all of the neat little jokes in there- all the little stuff like the "real shark" sign, and so on.
Alternatively you could try to compress it into something more feature-length... but honestly that'd be kind of disappointing, I'd wanna see all the neat little bits, personally. They make it what it is, in a lot of ways.
As for whether Telltale approves, I don't know, but that's a good question and I hope you get an answer.
...if you want to go for extra silly points, you could try to edit this in, but I'm not sure if it's such a good idea.
http://www.youtube.com/watch?v=zgRrM-gsE38