It can't. An online class is, even under the best of conditions, a weak half-brother to a brick and mortar, face-to-face class.
If a Katrina type disaster should blow a college away, perhaps the college could joint venture with The University of Phoenix until back on its feet.
I'm an "early pioneer" in our college system in the integration of teaching/learning technologies into our college environment; even as a "promoter" I have also been an educated skeptic, aiming to discern for quality, usability, and learner-centered practicality. From this vantage point I can not understand a generalization as you have so broadly stated it, that "An online class is, even under the best of conditions, a weak half-brother to a brick and mortar, face-to-face class." An online class is as good (or poor) as you make it, just as an on-ground class. And given the context--a natural disaster like Katrina--it seems to me it is only a matter of creativity and motivation that will limit whether people could use such avenues for continuing to teach well.