Not really. The cowl drain is on the outside of the firewall so, even without the tube, it will not let water get inside. What the tube does do is direct the water down, past the engine, without spraying water all over your electrical connections and other places you would prefer not to have too much water added
@Djobe478, the part you have was pitted against the power of the TJ exhaust heat and has not fared well. This is why everyone has been referring you to replacement parts. You will also want to get the foam gasket/seal that sits on the top and seals against the bottom of the opening in the cowl when the tube is in place.