It depends on the quantity of water. If a lot of water gets into a steamed pudding while it is cooking, it will be soggy. If only a small amount of water has leaked in, the pudding may be affected only in a small area and will still be palatable. The best advice is to try to stop water getting into the pudding by covering it properly. Traditionally, steamed puddings are cooked in a deep bowl or basin that is covered with a piece of greased greaseproof or baking paper, pleated in the middle and topped with a cloth, or a piece of pleated foil tied securely with string. The pleats allow room for expansion when the pudding is cooked. The covering is needed to keep the pudding well protected from the boiling water beneath, so that it is cooked in the steam and is moist but not sodden.
When steaming puddings, do not let the water boil too furiously as this will make it lap over the top. Keep it at an even rolling boil, or boil the pudding in a slow cooker.