Energy industry could easily build such a "Ike Dike" but why should the city of Houston do such a thing? Bush lobbied strongly for it on behalf of the energy guys, but didn't get it. Now you see why.
In the broad sense that's totally correct: weather will still be weather, and the sensor data & computing resources we have to throw at prediction are only getting better.
One aspect of this specific conversation relating to climate change, though, would be the relative abruptness of multiple weather systems combining into much larger storms. Sandy, for example, became a Frankenstorm in part due to multiple slightly abnormal factors coming together. That trend should erode predictability across multiple axes.
On the order of centuries, compared with the otherwise ability to predict weather: I would expect to see a marginal decline in weather predictability as more events, and more extreme events, are added to the atmospheric system.