Super Mario the Hedgehog
...I've been looking forward to it.
We don't know if there is a running option, but it has been confirmed that if you run out of stickers, you can't attack. I think there will be a running option, but I don't see the door being the tool needed for this feature as Bill tried to hide its purpose during his E3 playthrough on stage. I doubt you would try to hide that you can run from battles like every other installment, or RPG title in general.