No, it will not fire with a back on but no film. In this state, by holding the Mode button and pressing the arrow buttons, it is possible to switch the mode between B, 60 and M 1000, which is shown on the LCD. To fire the camera without film, you have to remove the insert. The camera then fires at B, 1/60 s or 1/1000 s, respectively.
Or alternatively, if you have the special cover for the back it will allow the camera to dry fire.
As as for the question about firing without a lens, I think I remember doing that, but I don't have my 645 with me now so I can't confirm it. But if I remember correctly, removing the lens does not make dry firing impossible.