Well a SIM would only make a difference if the phone needs it to turn on. Even if the SIM is not working (no service) some phones just need a physical SIM inserted to work. If yours does, then you would need one to insert. If not, then all you need is to be able to turn it on.
That said, if the display is broken, and you can't see to access things, or it won't turn on, then you won't be able to get the messages off the phone.