Well you can't screw attack through the ceiling in the room just to the right of the room that you fought BOX in, because you don't have screw attack yet. And you can't go up the same way you came in to the BOX room because you fell through a column of crumble blocks. I'd say the only way to go back up after the box fight is through the restricted lab. Fusion's like that.
Yeah, You'd need to cheat. That's the only way up. I'm also sure that he would say somthing about the restricted zone. With that you must go through the Restricted zone.
I doubt very much that he would, DB. PJBoy's event list (which is lots of fun) lists all the possible values of the event counter, including Adam speeches that speedrunners rarely see because we go straight to the target. He doesn't list any new Adam speeches between events 58 (wave beam) and 5F (post-restricted zone). So even if you could reach a Navigation Room, you'd just get the "Is your objective clear? Go kill BOX" routine. You could find out for sure with cheat codes, but it wouldn't be a good use of time.
The rule of sequence breaking is you have to complete the current objective. If you don't complete it, it will just continue to tell you too. If you skip to the following one, it will say 'Target Eradicated'