In short, yes you can copy a key that is broken in half. However, there are a few things you need to take into account before doing so.
If the break is clean and straight, then it should be a relatively simple process. Simply place the two halves of the key into a key duplicator and make sure they are lined up correctly. The machine will do the rest.
However, if the break is jagged or otherwise not clean, then it may be more difficult to get an accurate copy. In this case, you may need to file down the edges of thekey so that it fits snugly into the duplicator. If done correctly, you should still be able to get a perfect copy of your key.