YouTuber JerryRigEverything has a fun video I linked above where he unboxes the NES Classic and then opens it up to examine the mainboard and components. As you can see, it's a system that is very well integrated and I don't immediately see how you could hack this thing from the mainboard. That said there might be a couple methods depending on what Nintendo has allowed over the controller port OR back USB port. People are already hacking Linux on these things, which is a good sign but so far it requires some main board soldering.
Regardless of if you want to hack it what's included is incredible and I can't wait to pick one up. If I am able to get my hands on one before the holidays i'll let you know and if you get one i'd love to hear your thoughts on it and how you picked it up.