Can drinking 1 litre of water at one go cause diarrhoea?

In some: People, yes it can. Why would you drink that much at one time?

Not likely: The water does not "go through you" but is slowly absorbed by your digestive tract. If you are already well hydrated, you will more likely need to urinate quite a bit. You could have a looser stool as the large intestine normally absorbs water. Diarrhea or a watery, unformed stool is less likely.