It's possible, but the tricky part is to identify this "non-activity"... What would trigger starting it, and ending it?
Anyway, what's the point of such a feature? I think it will only confuse users if they open a file to a certain page, go to make a cup of coffee, and come back to find it jumped to another page on its own, don't you think?
Honestly, you don't want to use Acrobat as the runtime for this sort of application. You might want to use a PDF as the input but you're going to want to create a custom viewer that can interpret more kinds of touch than Acrobat currently has.