Nothing. Including the date doesn't do anything other than commit yourself to stating that date, the important part is the date at which you commit to the hash.
I'm assuming to you add the document (with date) to IPFS without being connected to the network (no actual data gets shared, only hash), gets the hash and send it over to the person you need to prove the document's date to. They won't be able to get it (since content itself is offline) and once you want to prove it, you add it again or make it otherwise online. Then they can fetch the same hash and confirm they received the hash at the date.
