You are not required to beat Withered mode I don't think. Considering you can unlock Pizza Party without beating it, it appears you most likely don't have to beat it here either. I think its just an extra thing they added to the game for fun.

You are able to skip the roller coaster on PC for both non-VR and VR. You can simply pause the game as soon as the intro starts and press quit to menu. Which then takes you to the main hub.