I was a Disaster Preparedness O at NASP when I was on shore duty. Which around there pretty much means hurricanes. Even with zero damage, a hurrevac shuts down the base completely for 4-5 days - they have to secure the utilities and buildings before everyone skedaddles, and it takes time to turn all that back on. CC has some mess to clean up but that's about all. If you were reporting to Wing Four in the next few weeks it might impact you.
If anything might slow down training (and again, not for the OP, but may have ripple impacts for the next few months) is relief support staging. We looked at how it'd impact P'cola if we had to support relief ops, like the base did for Katrina. Similar situation in Texas now; military airbase with nice long runways immediately down the coast from the disaster zone and didn't take much damage. P'cola looked like a Berlin Airlift reenactors' convention after Katrina.