I don't think it will in it's current state. Though we don't know much about it, I doubt it would have more than 8GB or 16GB of storage on it. And it probably won't go a week on a charge like my Classic.
That and running a cable to your wrist just doesn't make sense and would be in the way. Unless it was bluetooth, but I'm guessing it may already be connected to said iPhone with bluetooth, so it wouldn't connect to the headphones, unless it can do two at once. But then if you have an iPhone you'd just use that for music.
To be able to replace the iPod it would have to be able to be used as a standalone device without an iPhone attached. And have ample storage, along with a long lasting battery. Probably not going to happen.
Now years down the line with improvements in technology, better battery tech, better, higher capacity NAND, and screen tech. Sure, it may be possible. But for the first gen, I doubt it.