score:5
It would really depend on the hotel, and their terms and conditions. More than likely, you'll probably be charged for a full night as the hotel will find it hard to sell the room once you all depart.
Upvote:6
Milano Centrale station has a [left luggage office(http://www.milanocentrale.it/en/service/detail/left-luggage1); for 9 hours the fee is €7.80. There are of course toilets (with a €1 fee), but unfortunately no shower. It seems that there is a wifi hotspot too, I can't find any information as to whether it's free.
While there are hotels in Milan with day rooms, you'd have to vacate the room by 18:00 at the latest. It doesn't seem worthwhile unless you really want to sleep.