HN is small enough that timing matters even more than on Reddit. So a script would have to take that into consideration. HN also works against duplicate posts, so a post at midnight US eastern time wouldn't see much activity, and then reposts later in the morning would only add to its upvotes rather than getting new (better timed) listings.
Yes, but limited. It'd depend on whether the mods reupped the post the next morning so it could have a chance of hitting the front page or if a dupe managed to get through (which does happen). Either because the system permits it, or because the submitter added a #nonce to the end.
If the mods reupped it, then it'd work out really well for the original submitter. If karma mattered, I suppose it'd be worth trying a few times to see how it worked out.
Yeah, I'm not going to bother with it just for imaginary internet points, but I bet if you wanted to take it further you could analyse the top sites that hit the front page and poll all of them.