I was thinking of shooting a sheep faraway from one end of the world to another. Though arrows can go that far, what if they do? And if they do, will they be able to hit the sheep that's standing in the unloaded area or chunk? Well, the real question is, is it possible to do any interactions to entities in unloaded chunks?
Unloaded chunks are, rather unsurprisingly, not loaded. This means they only exist on disk, not in memory. In order to do anything with them, they would first have to be loaded into memory, at which point you could no longer call them "unloaded chunks." So by definition, nothing interesting ever happens in an unloaded chunk.
(You probably could point an NBT editor at the unloaded chunks, but I wouldn't risk it. Shut down Minecraft before you try to edit its files, since it might decide to load chunks when you aren't expecting it.)
There is a way to shoot the faraway sheep. If the sheep is within a spawn chunk it will never be unloaded. Then you can go as far as you like and take your shot!