Basically, here it is. Did Bush cut the funding? Yes. Did it make a difference? No. It would take a few years for the study, which would bring it to about 2002-2004 for the study completion, then add the 20-25 years to actually do something.
So in short: No, the funding cut didn't affect it.
The floodwalls which breached, did so as the result of overflow waters that then eroded the ground underneath these walls. This danger was understood before the study you mention.
The failure here is that, prior to the hurricane actually happening, the probability of such a storm as Katrina was so low that there was no political willpower to divert monies for improving the floodwalls. Would this have been different under a Democratic administration and Congress? I don't know; but I do know that politicians who ignore dangers because of their statistical improbability, and then get stuck out in the rain when those dangers come to pass, deserve to be held responsible for failing to use their resources more wisely. Bush decided national disaster preparedness wasn't important, and now I and every other patriotic citizen is going to rake him across the coals for it. We have seen once and for all the result of four years of his administration's attempts to make this nation better able to cope with an emergency.
Let's be honest. If everything about this situation were the same, except that it was a Democrat in the White House and Republicans on the state and local level, you'd be blaming the man in Washington. That's the difference between us. I'd be blaming the guilty party; you're looking to blame liberals. The fact that Bush is at fault for this, rather than a liberal, is just one more incentive for me to prosecute the case against him with that much more zeal. I also understand that state officials bear some responsibility. Primarily, their guilt has to do with the lack of proper coordination. And the governor and senior senator are Democrats. Well, tough. They're in trouble too.
But the lion's share of this disaster is Bush's fault, and do not think that we're going to let you conservatives forget it. The dangers of floodwall collapse were known years in advance--decades, really--and the funding for improving those weaknesses could have been made available many years ago, rather than being cut.
Maybe or maybe not it would have made a difference in time for Katrina to strike...but it would have been the correct effort, and it would have relieved this administration of a big slice of its guilt.