Yes, I was able to get out of the spectator room. I did it by jumping into the window area, and by holding down jump, I was able to kinda hover against for a while until I finally went through. On one of the tries before that, when I hovered sideways into a post, it hurt me. I was able to do this another time by pressing forward and a sideways direction (such as W + A) while doing the hover, and I got through. However, when I did this with a shield up to prevent damage from hitting the edge of the open window, I got stuck.
Update: It seems it's different every time, as I was able to get down into the arena by using the shield once I started moving sideways towards the post.