you push the button on the right to release the plunger on the left and open the barn doors to let the lens/shutter extend. Pushing the plunger once after you do this advances the film and cocks the shutter. If you push it a second time without firing the shutter, it does not do either again, first you have to fire the shutter (button on the right again) and THEN push the plunger to advance/cock.
Yes it should do this even if the back is removed, BUT IT WON'T MOVE THE SPROCKET UNLESS YOU FIRE THE SHUTTER FIRST.
When you push the lens doors shut by pushing on the shutter housing, you then push the plunger down again to hide it away.