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You don't need 4 copies of the game if you want to play local co-op offline, you just need 1 copy of the game and 4 controllers (shared screen).
If you mean like offline LAN (not shared screen), I guess it will work just like it does for other games. Consoles will need to be linked via a router or cross-over LAN cable, they will then need to be configured in Network Settings to share the network IP.
That's as far as linking the consoles goes. As for linking the games, this will need to be a feature that the game allows and gives the option for.
I haven't actually seen any information on whether or not D3 will support LAN games so it's a good question. I'll post it to the stickied FAQ.
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