You can take control of the alien during cutscenes/parts where you don't have control if you game over before the cutscene. I doubt that could be used in many things, but I wanted to see what happens at the end of 1-1 if the bus comes through without the alien.
Nothing, it just keeps going. I might have been able to try starting 1-2 while game-overed but I didn't think it would still trigger. I guess that's technically faster as the bus doesn't stop, but the fact that you need a precisely timed game over might not be worth it, saving a second on the cutscene but killing the boss much later.