The straight answer to this is - No.
Killing the boss only gives you the head, and the antlers. If you've mounted the head and selected the buff... and have the antler pick-ax or progressed to the bronze pick-axe, you can very well start another world and skip the first boss.
Actually killing the boss doesn't do anything to progress the game (other than trigger certain raids).
The only reason you might want to kill a boss again, is if you have a different boss buff selected, and want to change to a previous boss buff you don't have the head mounted.