Hmmm. Not quite. The bullet and the case will hit the ground at the same time IF the rifle barrel is horizontal, AND the fired case goes directly out of the action and straight down. But that never really happens since the case is first trapped in the bolt, usually begins by going upward, etc., so the bullet gets a head start on the bolt.
HS physics teachers keep a neat little gadget around to show the the action; not a gun, but a spring gadget that releases one ball to drop down and a second to fly out some distance after being struck at the same time.
Jim